Quantitative study on the homogeneity of networks synthesized by nitroxide-mediated radical copolymerization of styrene and divinylbenzene

Accepted Manuscript Quantitative Study on the Homogeneity of Networks Synthesized by NitroxideMediated Radical Copolymerization of Styrene and Divinylbenzene Shaghayegh Hamzehlou, Yuri Reyes, Jose R. Leiza PII: DOI: Reference:

S0014-3057(16)30675-9 http://dx.doi.org/10.1016/j.eurpolymj.2016.10.015 EPJ 7552

To appear in:

European Polymer Journal

Received Date: Revised Date: Accepted Date:

1 July 2016 15 August 2016 9 October 2016

Please cite this article as: Hamzehlou, S., Reyes, Y., Leiza, J.R., Quantitative Study on the Homogeneity of Networks Synthesized by Nitroxide-Mediated Radical Copolymerization of Styrene and Divinylbenzene, European Polymer Journal (2016), doi: http://dx.doi.org/10.1016/j.eurpolymj.2016.10.015

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Quantitative Study on the Homogeneity of Networks Synthesized by Nitroxide-Mediated Radical Copolymerization of Styrene and Divinylbenzene

Shaghayegh Hamzehlou1, Yuri Reyes2, Jose R. Leiza1* 1

POLYMAT, Kimika Aplikatua saila, Kimika Zientzien Fakultatea, University of the Basque Country

UPV/EHU, Joxe Mari Korta Zentroa, Tolosa Hiribidea 72, 20018 Donostia-San Sebastián, Spain

2

Departamento de Recursos de la Tierra, Universidad Autónoma Metropolitana Unidad Lerma (UAM-

L). Av. Hidalgo 46, Col. La Estación, CP 52006, Lerma de Villada, México.

*Corresponding author: [email protected] Abstract The nitroxide-mediated radical copolymerization (NMRP) of styrene and divinylbenzene was studied using a Monte Carlo simulation. The model predictions were validated by comparing to experimental results gathered from literature. Polymer network microstructure was studied through complete molar mass distribution (including the gel part) of the polymer and by quantitative representation of the homogeneity of the network, i.e. the broadness of the distribution of the molar mass between crosslinking points (Mc). The nitroxide mediated radical polymerization led to a narrower Mc distribution compared to free radical polymerization, and the average Mc did not change significantly through the reaction. The narrower Mc distribution is an indicator of more homogenous network and clarifies many conflicting statements in the literature on homogeneity of the network obtained by controlled radical polymerization.

Keywords: controlled radical polymerization, crosslinking, network homogeneity

Introduction Crosslinked polymers have been a subject of continuous interest since the beginning of polymer

1

science, ranging from their synthetic routes to the applications, and of course, their characterization. A crosslinked polymer is formed by a three dimensional network in which all of its constituents are linked; this complex structure is the responsible of the properties of the crosslinked polymers, such as thermal stability, swelling with a solvent (but not dissolving), resistance against alkali and acids, elastic behavior, etc.[1–5]In conventional free radical polymerization crosslinked polymers can be synthesized by copolymerizing a monovinyl monomer in the presence of a rather small amount of divinyl monomer, which is the responsible of linking different chains during the polymerization yielding to the polymer network. In a polymer network the molar mass between crosslinking points, Mc, dictates most of the properties of the network together with the pendant chains (chains that are connected to the network with a single point and do not participate in the mechanical properties). Additionally, short loops formed by cyclization reactions, i.e. a polymer chain that reacts with a pendant double bond (PDB) on its growing chain, decrease the mechanical performance of the network. The advent of controlled radical polymerization (CRP) techniques allowed the synthesis of polymers with a narrow molar mass distribution and more complex polymer architectures. Such polymerization technique was used also to obtain polymer networks in both homogeneous and heterogeneous systems aiming at forming more homogeneous networks. Thus, nitroxide mediated radical polymerization (NMRP) [6–9], atom transfer polymerization (ATRP)[10–12] and reversible addition fragmentation chain transfer polymerization (RAFT)[13,14] have been used for this purpose. In general these works reported lower rate of polymerization, delayed gelation, higher swelling and better molar mass control than in the counterpart experiments carried out by FRP.[14–18] Specifically on NMRP, Fukuda and Ide investigated the copolymerization of styrene and 4,4´-divinylbiphenyl. The apparent pendant vinyl reactivity was considerably lower in the controlled/living system than in the conventional system before the gelation, which led to much slower rate of polymerization in CRP. The authors suggested that the gels prepared by this method may be much more homogeneous with less cyclization than those prepared by the conventional free-radical method. The molar masses between crosslinking points were calculated according to Flory and Rehner theory, and it was claimed that the Mc is much higher for NMRP as compared to the FRP and has a stronger dependency on the conversion, however Mc values were shown only at low and small range of conversions.[19,20] Similar arguments were given in the literature e.g. much shorter primary chains in CLRP result in less intra-molecular crosslinking and minimize the formation of microgels, without any clear proof. [7] On the other hand, the correlation between synthesis variables and network properties is not an easy task, due to the inherent insolubility of polymers with a very high molar mass (approximately more 2

than 107 g/mol), which are commonly called gel polymer. From the experimental point of view, the average molar masses and the distribution of the molar masses of the soluble fraction can be determined, as well as the swelling of the polymer network by a solvent and the weight fraction of soluble and insoluble polymers. With more sophisticated techniques the pore size within the polymer network can be inferred.[21–23] Because of these limitations and because a network is intrinsically interesting, mathematical descriptions and modeling have been widely used and developed to study polymer networks.[24–27] Within the modeling approaches, Monte Carlo simulation is a technique that allows a deep description of the network structure because the detailed microstructure of chains can be followed during the polymerization.[28–36] Such simulation approach has been tested and it has been demonstrated that it is capable of providing the same results than other simulations approaches, but additionally providing information that is elusive for other deterministic simulation techniques.[37–39] Detailed kinetic models were developed to model nitroxide-mediated radical copolymerization of vinyl/divinyl monomers, however the prediction of the microstructure of the networks provided by these models was limited to average values such as, gel fraction, average molar masses of the sol part, primary cyclization and crosslinking density but no information on Mc and its distribution was provided in any of them.[40–42] In this contribution a Monte Carlo algorithm (MC) was developed to simulate the nitroxide-mediated polymerization (NMRP) of styrene (S) and divinylbenzene (DVB).This study is an extension of a recent modelling approach[37] developed to accurately predict the complex microstructure of polymer networks produced by free radical crosslinking copolymerization. The predictions of the model are validated by comparison with experimental results available in the literature for the S/DVB NMRP copolymerization. As mentioned above one of the most important ongoing discussions on the synthesis of polymer networks by CRP is the homogeneity of the network, i.e. the broadness of the distribution of the molar mass between crosslinking points, which cannot be accessed experimentally. It is usually claimed that in CRP the polymer network is more “homogeneous” with limited intramolecular crosslinking (or cyclization) as compared to the FRP, in which local inhomogeneity in terms of the distribution of unreacted pendant double bonds favours cyclization.[19] To the best of the authors’ knowledge such assumption has not been totally validated, neither by experiments nor by simulation. Only indirect evidences have been presented in the literature i.e. conversion of PDBs, swelling ratios and average molar mass between crosslinking points ( experiments. [19,20,43] However,

), that is calculated based on swelling

is an average value and does not give any information about its

distribution, which basically is an indicator of the homo- or heterogeneity of the network. A more 3

comprehensive study is needed to clarify many conflicting statements in the literature regarding the homogeneity of the network obtained by CRP. In this work, with the help of MC simulation, we are able to get very detailed information of the microstructure of the polymer network, which provides quantitative data on the homogeneity of the network in NMRP of S in the presence of the DVB crosslinker. Simulation details Kinetic scheme The nitroxide mediated polymerization of S and DVB is considered in this work. The kinetic scheme used in the simulation is presented in Scheme 1. The kinetic scheme was adopted from the work of Scott et al. [43], which comprises dimerization, thermal initiation of S, unimolecular initiation, initiation by propagation, propagation, reversible deactivation of polymer radicals, propagation to PDB and termination by combination (that is the preponderant termination mechanism in styrene polymerization).[44,45] For simplicity, chain transfer to monomer and chain transfer to polymer were not considered. For this work any diffusional or geometrical constraint effect was not implemented in the model. Diffusion

controlled effects were assessed by Hernandez-Ortiz et al.[40] and found

unimportant in the NMRP of S and DVB.

Nevertheless, this kinetic scheme contains the most

important features in the formation of the polymer network in the radical polymerization of S/DVB system.

Scheme 1. Kinetic scheme of the nitroxide-mediated radical copolymerization of S/DVB considered in the simulation. Dimerization:

Thermal Initiation:

Unimolecular initiation:

Initiation:

4

Propagation:

Reversible deactivation of polymer radicals:

Termination by combination:

5

Propagation to pendant double bond (crosslinking, primary and secondary cyclization ):

M1: S monomer; M2: DVB monomer; M3 :DVB monomer incorporated in polymer chain having pendant double bond (PDB); I: initiator; Ri,1:chain-end radical of monomer 1 with length i; Ri,2:chain-end radical of monomer 2 with length i. Ri,3:chain-end radical of PDB of monomer 2 with length i. D: is the dimer. : dimeric radical; : alkoxyamine, : nitroxyl radical; : dormant polymer with chain length i and deactivated radical center type 1; : dormant polymer with chain length i and deactivated radical center type 2;

The values of the kinetic coefficients used in the MC simulation are reported in Table 1 which were mainly taken from the work of Scott et al.[43] or references therein. A unimolecular initiator N-tertbutyl-n-(2-methyl-1-phenylpropyl)-O-(1-phenylethyl) hydroxylamine (referred as I-TIPNO) was considered in the mentioned reference. Decomposition of this alkoxyamine, produces 2,2,5-trimethyl4-phenyl-3-aza-hexane-3-nitroxide which is referred to as TIPNO nitroxide.

Table 1. Kinetic coefficients used in the MC simulation of the nitroxide-mediated S/DVB bulk crosslinking copolymerization Rate Constants Reference [43,46] [43] [43] [43] [43] [43] [47] 6

[24] [48] [49] [48] [49] [43] [46]

Monte Carlo simulation The details of the MC simulation for the crosslinking copolymerization of S and DVB were described in previous works.[37,39]Here, we briefly explain the important aspects of the simulation; for more details the reader is referred to the mentioned references. The full kinetic Monte Carlo approach proposed by Gillespie was implemented.[50,51] This simulation method employs a control volume, V, which must be defined. The selected control volume is L; as it was demonstrated in previous works, this control volume is large enough in order to decrease the effect of the size of the system while obtaining reliable statistical results.

Initial

concentration of the reactants must be defined as well. Then, by using the Avogadro's constant, the number of molecules of each reactant is established. In order to calculate the possible combinations of the proposed reactions, stochastic rates and rate coefficients were defined.[52,53] The reaction to occur was selected randomly using the cumulative probability of reaction rates. The time that this reaction consumes is obtained from a logarithmic distribution. Dimerization and thermal initiation leads to the appearance of radicals that can later propagate. The information of each created polymeric radical was followed and saved individually. In the case of deactivation of the polymeric radical with nitroxyl radical a dormant chain with the same chain length was created which later could be activated again. In the case of the propagation to a PDB or termination that results to linking of two chains, the connectivity information was saved. The connectivity information is then analysed by a sorting/searching algorithm to identify the chains that are linked forming the clusters, i.e. a collection of polymer chains that are directly or indirectly linked.[37] As the information of the individual chains is saved during the simulation, by knowing which chains form the clusters, it is possible to determine the cluster properties, such as molar mass, composition, crosslinking density (the ratio of the number of crosslinking events to the total propagation steps) and molar mass between crosslinking points. On the other hand, as no geometrical constraint was imposed, it is possible to access any PDB in the 7

considered control volume (it can be in the same chain or in the same cluster or in another chain with already minimum one active site), therefore primary and secondary cycles and multiradicals were considered naturally in the model (Figure 1). It is worth mentioning that for all the reactions that imply a propagation to pendant double bond reaction (i.e., primary and secondary cyclization and crosslinking reactions) the same kinetic rate constant was considered (

in Table 1) because no geometrical

constraint was considered in the model. By using the proposed approach, no additional simplifications are needed to determine the entire molar mass distribution (and the molar mass averages), the composition of each polymer chain and crosslinking density. Because the positions of reacted PDBs were tracked on the individual chains, the complete distribution of molar masses between crosslinking points was obtained. This detailed information of the microstructure of the polymer network will shed light on the homogeneity of the network. The simulations are the average of 100 independent runs, coded in Fortran under Linux. Each single run took 1.5 hr in a PC with 16 cores Intel(R) Xeon(R) CPU E5620 @2.40 GHZ. The code has not been parallelized and only standard optimization options of the compiler were used.

Figure 1. Schematic reactions of A) cyclization B) crosslinking C) multiple crosslinking and multiradical formation Results and discussion Model validation The batch bulk polymerization of the S/DVB in the presence of I-TIPNO at 120C was considered in the simulation. Table 2 presents the details of the experiments carried out by Scott et al.[43] that were 8

considered in this work to validate the model. Note that the ratio between DVB to I-TIPNO is 2.5 and 1.87 for experiments 1 and 2 from Table 1, respectively.

Table 2.Formulation of the NMRP of S/DVB carried out in reference [43] and simulated in this work. Experiment Temperature(°C) I-TIPNO(mol/l) DBV(mol/l) S(mol/l) 1 2

120 120

0.027 0.056

0.06750 0.10472

7.79 7.79

The simulation predictions are the average of 100 independent runs, which give reliable statistical results. Here we show briefly the validation of the NMRP simulation by comparing the MC simulation predictions with the experimental data gathered by Scott et. al.[43] It is worth mentioning that the aim of this work is not the accurate prediction of the experimental data, but implementing the modeling approach to shed light on the uncertainties reported in the literature regarding the homogeneity of the polymer network obtained by the NMRP as compared to conventional FRP. Figure 2 shows a comparison of the MC simulation prediction of conversion vs time for the two experiments described in Table 2, carried out with different amounts of crosslinker (DVB) and alkoxyamine. It can be seen that the simulation reproduces the experimental conversion evolution rather good. a) 1,0

Conversion

0,8 Exp. 1 model

0,6

0,4

0,2

0,0 0

5

10

15

Time(hr)

9

20

25

30

b) 1,0

Conversion

0,8

Exp.2 model

0,6

0,4

0,2

0,0 0

5

10

15

20

25

30

Time(hr)

Figure 2. Comparison of model prediction and experimental data on conversion gathered from reference [43] for experiments 1 and 2 from Table 2.

The predictions for gel fraction and molar mass for the same reactions together with the experimental values reported in reference [43] are shown in Figure 3 and 4, respectively. It can be seen that the simulation predicts slightly earlier the gelation but captures very well the experimental trend during polymerization. Note that as explained in references [37] and [39] the MC simulation uses a threshold value to determine which molar masses of the chains belong to the gel, i.e. the chains with molar masses higher than 107 g/mol were considered to be gel polymer. This threshold value is not universal and it might be determined experimentally for each system (e.g., analyzing by SEC the maximum molar mass of the soluble polymer). The value used in this work (107 g/mol) provided reasonable predictions of gel and sol MMD for other experimental systems.[54] The same trend can be seen in the average molar mass predictions. Note that the threshold value might affect the sol molar mass predictions as it defines which chains are part of the gel and which are not. Nevertheless, the model captures well the experimental data before gelation and the trends after gelation. As discussed above the goal of this work was not to fit accurately the experimental results, but to shed light on the final microstructure of the polymer networks produced in the presence of 10

controlling agents like nitroxides and providing quantitative information on the microstructure. Furthermore, we aimed to improve the knowledge on the formation of the complex polymer network in order to avoid the speculative, ambiguous and uncertain explanations provided so far in the literature. Note that experiment 1 used 1wt% of crosslinker while experiment 2 used 1.5 wt%, however gelation occurs at lower conversions for experiment 1. Faster gelation in experiment 1 is due to the higher ratio of the crosslinker to TIPNO which is 2.5 for experiment 1 and 1.87 for experiment 2. The effect of the control agent on retarding gelation is well known in literature.[29,36,38,55] The model captures well this delayed gelation observed in experiment 2.

a) 100

Exp. 1 Model

gel fraction

80

60

40

20

0 0,0

0,2

0,4

0,6

0,8

1,0

Conversion

b) 100

Exp. 2 Model

gel fraction

80

60

40

20

0 0,0

0,2

0,4

0,6

Conversion

11

0,8

1,0

Figure 3. Comparison of model prediction and experimental data on gel fraction gathered from reference [43] for experiments 1 and 2 from Table 2.

100M 10M

Exp. 1

1M

Mn,Mw(g/mol)

100k 10k 1k 100 10M

Exp. 2

1M 100k 10k 1k 100 0,0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1,0

Conversion

Figure 4. Comparison of model prediction and experimental data on number and weight average molar mass of the sol fraction gathered from reference [43] for experiments 1 and 2 from Table 2. Filled circles are Mn experimental data points, hollow circles are Mw experimental data points from reference [43]. Dashed lines are Mn model prediction and solid lines are Mw model prediction. Detailed simulation of the network microstructure The complete molar mass distribution can be obtained by MC simulation. Figure 5 shows the molar mass distribution (MMD) of the polymer through the reaction for the experiments presented in Table 2. For comparison purpose the MMD of the FRP of S/DVB at 100C with 1wt% of DVB and benzyl peroxide as an initiator is also included in Figure 5.[37] Note that in order to take into account the effect of the instrumental broadening caused by axial dispersion in the SEC instrument, all MMDs obtained by MC simulations are convoluted with a Gaussian function featuring a standard deviation of 0.1, which is in the acceptable range reported in the literature.[56–58] Increase of the molar masses until the gelation point is clearly represented in the MMD by shifting the distribution to the right hand side. After gelation two distinct peaks can be seen in the MMD; in which the peak at lower molar masses corresponds to the sol and the peak at higher molar masses corresponds to the gel. Although from the macroscopic point of view the peak in the large molar mass region is unrealistic for a bulk process, it is representative of the gel properties such as crosslinking density, pendant double bond density and molar masses between crosslinking points.[39] As the polymerization evolves the gel fraction increases as well as the molar masses of the gel. On the other hand the sol 12

fraction decreases and also the sol molar mass, but interestingly the position of the peak of the sol MMD is not affected significantly. The reason is that in CRP most of the chains grow more or less together; nevertheless the longer chains are the ones that are preferentially incorporated to the gel (they have more PDBs to react). It can be seen that only the right hand side tail of the sol MMD disappears through the reaction after gelation. The behavior is completely different in the FRP, in which after gelation (around 7% of conversion) the MMD of the sol part shows a significant decrease in the average molar mass of the sol (Figure 5c), because shorter chains remain as soluble due to their lower probability to be linked into the gel chains. Note that in FRP the kinetic chain length of individual chains also decreases as the polymerization evolves. a) 3,0 5% Conv. 20% Conv. 40% Conv. 60% Conv. 70% Conv. 80% Conv. 90% Conv.

2,5

W(logM)

2,0

1,5

1,0

0,5

0,0 2

4

6

logM

b)

13

8

10

3,0

5% Conv. 20% Conv. 40% Conv. 60% Conv. 70% Conv. 80% Conv. 90% Conv.

2,5

W(logM)

2,0

1,5

1,0

0,5

0,0 2

4

6

8

10

logM

c) 3,0 1% Conv. 2% Conv. 3% Conv. 5% Conv. 10% Conv. 20% Conv.

2,5

W(logM)

2,0 1,5 1,0 0,5 0,0 2

3

4

5

6

7

8

9

10

log M

Figure 5. Molar mass distribution evolution a) NMRP of experiment 1 from Table 2 b) NMRP of experiment 2 from Table 2 c) free radical polymerization from ref [37] with 1 wt% DVB.

Figure 6 shows the evolution of the distribution of molar mass between crosslinking points (corresponding to all the polymer chains; sol and gel) through the reaction for experiments 1 and 2 from Table 2 and FRP with 1wt% of DVB from reference [37]. In Figure 6a, at low conversions, Mc shows a large dispersion and it can reach up to 1000 monomer units. As the reaction evolves, there is an increment of the concentration of chain segments with smaller Mc, and some of the largest Mc disappear, since PDB located in between are consumed reducing the distance between crosslinking 14

points. This trend goes on and, at high conversion the concentration of chains with Mc larger than 700 monomer units is negligible and small Mc values are predominant. The distribution becomes narrower by increasing weight percentage of the controller (experiment 2 with 2wt% of I-TIPNO) since the chain length of the individual chains is smaller as the concentration of I-TIPNO is higher in this experiment, on the other hand higher crosslinker in this experiment (1.5wt% crosslinker) leads to a tighter network. Interestingly, the place of the peak does not change significantly through the reaction for CRPs experiments. In the case of FRP (Figure 6c) with 1wt% crosslinker the distribution is much broader (chains with Mc’s of up to 4000 monomer units at low conversion). As the conversion evolves, the distribution shifts to the lower values with an increment at lower Mc values, however this trend is more pronounced here comparing to CRP. This suggests that in the FRP at lower conversions a lose network was formed; while PDBs located in between are consumed, the network becomes tighter and this change is significant through the reaction. To have a quantitative representation of the homogeneity of the network Mc dispersity index (DI) and the upper limit of the distribution is presented in Table 4 at 90% of conversion for all experiments. It can be seen that FRP has higher DI comparing to the NMRP, and much higher upper limit of the distribution which indicates a narrower distribution and a more homogeneous network in NMRP comparing to the FRP.

a) Concentration(mol/L)*Distance

0,009 0,008

50% conv. 60% conv. 70% conv. 80% conv. 90% conv.

0,007 0,006 0,005 0,004 0,003 0,002 0,001 0,000 50

100 150 200 250 300 350 400

900

950

Distance between crosslinking point (Chain length)

b)

15

1000

Concentration(mol/L)*Distance

0,009 0,008

50% conv. 60% conv. 70% conv. 80% conv. 90% conv.

0,007 0,006 0,005 0,004 0,003 0,002 0,001 0,000 50

100

150

200

250

950

1000

Distance between crosslinking point (Chain length)

Concentration(mol/L)*Distance

c) 0,009 0,008

20% Conv. 40% Conv. 60% Conv. 80% Conv.

0,007 0,006 0,005 0,004 0,003 0,002 0,001 0,000 0

100 200 300 400 500 600 700 800 900 2000

3000

4000

5000

Distance between crosslinking point (Chain length)

Figure 6. Mc weight distribution evolution a) NMRP of experiment 1 from Table 2 b) NMRP of experiment 2 from Table 2 c) free radical polymerization from ref [37] with 1wt% DVB.

Table 4. Dispersity index of the Mc distributions of NMRP of experiment 1 and 2 from Table 2 and FRP from ref [37] with 1wt% DVB. Experiment:

NMR (Exp. 1) NMR(Exp2)

FRP

DI of Mc at 90% Conversion

1.82

1.8

2.02

The upper limit of distribution (chain length)

642

383

1793

Figure 7 summarizes the substantial differences found on the microstructure of the crosslinked polymers produced by NMRP and FRP. Notably, the weight average

16

) is smaller in NMRP than in

FRP during the whole polymerization. Whereas in FRP, at low conversions, the distribution is broad, in NMRP the

is large and the

values are 2-3 times smaller (depending on the amount of the

nitroxide employed in the experiment) and the distributions are narrower. As monomer conversion increases the

values decreased in both cases but the decrease is monotonous over the entire reaction

in FRP while in NMRP is modest and once gelation occurred the

remained almost constant. The

dispersity of the distribution of the Mc is broader for FRP than for NMRP and within the later the higher the concentration of the nitroxide the narrower the distribution and hence the more homogeneous the polymer network obtained. Figure 7 also plots the average chain length between crosslinking points calculated assuming a homogeneous distribution of the crosslinking points in the polymer chains; namely:

This equation is widely used in the deterministic models reported so far in the literature to compute the average chains length between crosslinking points (or the crosslinking density, which is the inverse of this value). As discussed in reference [37] the calculated from the distribution. Figure 7 plots the

differs substantially from the average value value for the FRP reaction and for the

NMRP (Exp. 1) case. For the FRP the discrepancy is large at low conversions and seems to converge at large conversions, but the trend is similar; a monotonous decrease of

as conversion increases during

reaction. However, for the NMRP the discrepancy is large for the whole process, being the

value

substantially larger when it is assumed that the crosslinking points are equally distributed in the chains. The

values not only overestimate the real

but also provided a wrong evolution of the

formation of the crosslinking points in the reaction. Indeed, the

values at low conversions are

as high as the average chain length of the soluble chains which is unrealistic.

cannot be as high as

the kinetic chain length of the individual chains, therefore, the number of monomer units between crosslinking points is much shorter in NMRP comparing to the FRP. However, if the

is calculated

as the inverse of the crosslinking density, such calculation does not consider this fact. Finally it is worth mentioning that as no geometrical and accessibility constraints were considered in the model, the cyclization reaction is almost negligible and underestimated in FRP (about 0.01% of cyclization to crosslinking reaction)[37], nevertheless in NMRP no multiradicals and almost no cyclization were formed which is a demonstration of lower intramolecular reactions in the NMRP comparing to the FRP. The Model prediction can be a reasonable guide to show the differences between FRP and NMRP

17

but cannot be taken as a quantitative measurement on cyclization.

1300 1200 1100

NMRP Exp. 1 NMRP Exp. 2 FRP 1wt% DVB FRP 1wt% DVB ,Mc_homo NMRP Exp. 1 ,Mc_homo

1000 900 800 700

Mc 600 500 400 300 200 100 0 0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1,0

Conversion Figure 7. Weight average chain length between crosslinking points (

.

Conclusions The nitroxide-mediated radical copolymerization (NMRP) of styrene and divinylbenzene was studied using a Monte Carlo simulation. Polymer network microstructure was studied through complete molar mass distribution (including the gel part) of the polymer and by quantitative representation of the homogeneity of the network, i.e. the broadness of the distribution of the molar mass between crosslinking points (Mc). The nitroxide mediated radical polymerization led to a narrower Mc distribution compared to free radical polymerization, and the average Mc did not change significantly through the reaction and its evolution is totally different from the FRP one after gelation. The narrower Mc distribution is an indicator of more homogenous network in CRP compared to FRP. The results are also applicable for polymer networks produced by other CRP techniques like ATRP, RAFT, ect.

Acknowledgments The funding by the University of the Basque Country UPV/EHU (UFI11/56), Basque Government (IT303-07) and MINECO (CTQ2014-59016-P) are acknowledged.

18

References [1]

P.J. Flory, Principles of polymer chemistry, Cornell University Press, New York, 1953.

[2]

L.H. Sperling, Interpenetrating Polymer Networks and Related Materials, Plenum Press, New York and London, 1981.

[3]

K. Dusek, H. Galina, J. Mikes, Features of Network Formation in the Chain Crosslinking (Co)Polymerization, Polym. Bull. 3 (1980) 19–25.

[4]

O. Okay, Macroporous copolymer networks, Prog. Polym. Sci. 25 (2000) 711–779.

[5]

E.S. Dragan, Design and applications of interpenetrating polymer network hydrogels. A review, Chem. Eng. J. 243 (2014) 572–590.

[6]

Y. Saka, P.B. Zetterlund, M. Okubo, Gel formation and primary chain lengths in nitroxidemediated radical copolymerization of styrene and divinylbenzene in miniemulsion, Polymer 48 (2007) 1229–1236.

[7]

M.N. Alam, P.B. Zetterlund, M. Okubo, Network formation in nitroxide-mediated radical copolymerization of styrene and divinylbenzene in miniemulsion: Effect of macroinitiator hydrophilicity, Polymer 50 (2009) 1632–1636.

[8]

M. Nur Alam, P.B. Zetterlund, M. Okubo, Network Formation in Nitroxide-Mediated Radical Copolymerization of Styrene and Divinylbenzene in Miniemulsion, Macromol. Chem. Phys. 207 (2006) 1732–1741.

[9]

P.B. Zetterlund, M.N. Alam, H. Minami, M. Okubo, Nitroxide-mediated controlled/living free radical copolymerization of styrene and divinylbenzene in aqueous miniemulsion, Macromol. Rapid Commun. 26 (2005) 955–960.

[10] Q. Yu, F. Zeng, S. Zhu, Atom Transfer Radical Polymerization of Poly ( ethylene glycol ) Dimethacrylate, Macromolecules 34 (2001) 1612–1618. [11]

C. Jiang, Y. Shen, S. Zhu, D. Hunkeler, Gel formation in atom transfer radical polymerization of 2-(N,N-dimethylamino)ethyl methacrylate and ethylene glycol dimethacrylate, J. Polym. Sci. Part A Polym. Chem. 39 (2001) 3780–3788.

[12] M. Mennicken, B. Maier, H. Keul, Synthesis of Polymers Containing Cross-Linkable Groups by Atom Transfer Radical Polymerization : Poly ( allyl methacrylate ) and Copolymers of Allyl Methacrylate and Styrene, Macromolecules 37 (2004) 8923–8932. [13] Q. Liu, P. Zhang, A. Qing, Y. Lan, M. Lu, Poly(N-isopropylacrylamide) hydrogels with

19

improved shrinking kinetics by RAFT polymerization, Polymer 47 (2006) 2330–2336. [14] V. Crescenzi, M. Dentini, D. Bontempo, G. Masci, Hydrogels based on pullulan derivatives crosslinked via a “living” free-radical process, Macromol. Chem. Phys. 203 (2002) 1285–1291. [15] Q. Yu, J. Zhang, M. Cheng, S. Zhu, Kinetic behavior of atom transfer radical polymerization of dimethacrylates, Macromol. Chem. Phys. 207 (2006) 287–294. [16] S. Abrol, M.J. Caulfield, G.G. Qiao, D.H. Solomon, Studies on microgels. 5. Synthesis of microgels via living free radical polymerisation, Polymer 42 (2001) 5987–5991. [17] V. Herrera, R. Pirri, J.M. Asua, J.R. Leiza, Morphology Control in Polystyrene/pol(methyl methacrylate) Composite Latex Particles, J. Polym. Sci. Part A-Polymer Chem. 45 (2007) 2484– 2493. [18] Y. Lin, X. Liu, X. Li, J. Zhan, Y. Li, Reversible Addition–Fragmentation Chain Transfer Mediated Radical Polymerization of Asymmetrical Divinyl Monomers Targeting Hyperbranched Vinyl Polymers, J. Polym. Sci. Part A Polym. Chem. 45 (2007) 26–40. [19] N. Ide, T. Fukuda, Nitroxide-controlled free-radical copolymerization of vinyl and divinyl monomers.Evaluation of Pendant-Vinyl Reactivity, Macromolecules 30 (1997) 4268–4271. [20] N. Ide, T. Fukuda, Nitroxide-controlled free-radical copolymerization of vinyl and divinyl monomers. 2. Gelation, Macromolecules 32 (1999) 95–99. [21] K. Saalwächter, W. Chassé, J.U. Sommer, Structure and swelling of polymer networks: insights from NMR, Soft Matter 9 (2013) 6587–6593. [22] Y.E. Shapiro, Structure and dynamics of hydrogels and organogels: An NMR spectroscopy approach, Prog. Polym. Sci. 36 (2011) 1184–1253. [23] I. Calvo, Mathematical Modeling of Emulsion Polymerization of Styrene Butadiene Acidic Monomers, PhD thesis, University of Basque Country, 2012. [24] J.C. Hernández-Ortiz, E. Vivaldo-Lima, A. Penlidis, Modeling of Network Formation in Nitroxide-Mediated Radical Copolymerization of Vinyl/Divinyl Monomers Using a Multifunctional Polymer Molecule Approach, Macromol. Theory Simul. 21 (2012) 302–321. [25] S. Zhu, E. Hamielec, R.H. Pelton, Modelling of crosslinking and cyclization in free-radical copolymerization of vinyl/divinyl monomers, Makromol. Chem. Theory Simul. 2 (1993) 587– 604. [26] K. Dusek, J. Somvarsky, Modelling of Ring-free Crosslinking Chain, Polym. Int. 44 (1997) 225– 236. [27] J. Somvarsky, K. Dusek, M. Smrckova, Kinetic modelling of network formation: Size-dependent 20

static effects, Comput. Theor. Polym. Sci. 8 (1998) 201–208. [28] J. He, L. Li, Y. Yang, Monte Carlo simulation on rate enhancement of nitroxide-mediated living free-radical polymerization, Macromol. Theory Simul. 9 (2000) 463–468. [29] F.A. Escobedo, J.J. De Pablo, Monte Carlo simulation of branched and crosslinked polymers, J. Chem. Phys. 104 (1996) 4788–4801. [30] H. Tobita, Monte Carlo simulation of emulsion polymerization-linear, branched, and crosslinked polymers, Acta Polym. 46 (1995) 185–203. [31] E. Jabbari, Monte Carlo simulation of tri-functional branching and tetra-functional crosslinking in emulsion polymerization of butadiene, Polymer 42 (2001) 4873–4884. [32] H. Tobita, A.E. Hamielec, Control of Network Structure in Free-Radical Crosslinking Copolymerization, Polymer 33 (1992) 3647–3657. [33] H. Tobita, N. Hamashima, Monte Carlo Simulation of Size Exclusion Chromatography for Randomly Branched and Crosslinked Polymers, Polym. Sci. Part B Polym. Phys. 38 (2000) 2009–2018. [34] H. Tobita, S. Zhu, Polyradical distribution in free radical crosslinking of polymer chains, J. Polym. Sci. Part B Polym. Phys. 34 (1996) 2099–2104. [35] H. Tobita, Molecular Weight Distribution in Random Crosslinking of Polymer Chains, J. Polym. Sci. Part B Polym. Phys. 33 (1995) 1191–1202. [36] H. Tobita, A.E. Hamielec, Modeling of network formation in free radical polymerization, Macromolecules 22 (1989) 3089–3105. [37] S. Hamzehlou, Y. Reyes, J.R. Leiza, A New Insight into the Formation of Polymer Networks: A Kinetic Monte Carlo Simulation of the Cross-Linking Polymerization of S/DVB, Macromolecules 46 (2013) 9064–9073. [38] A.L.T. Brandão, J.B.P. Soares, J.C. Pinto, A.L. Alberton, When Polymer Reaction Engineers Play Dice: Applications of Monte Carlo Models in PRE, Macromol. React. Eng. 9 (2015) 141– 185. [39] S. Lazzari, S. Hamzehlou, Y. Reyes, J.R. Leiza, M. Costa, R. Dias, et al., Bulk Crosslinking Copolymerization: Comparison of Different Modeling Approaches, Macromol. React. Eng. 8 (2014) 678–695. [40] J.C. Hernández-Ortiz, E. Vivaldo-Lima, L.M.F. Lona, N.T. McManus, A. Penlidis, Modeling of the Nitroxide-Mediated Radical Copolymerization of Styrene and Divinylbenzene, Macromol. React. Eng. 3 (2009) 288–311. 21

[41] M.A.D. Gonçalves, I.M.R. Trigo, R.C. Dias, M.R.P.F.N. Costa, Kinetic modeling of the molecular architecture of cross-linked copolymers synthesized by controlled radical polymerization techniques, Macromol. Symp. 291-292 (2010) 239–250. [42] L.G. Aguiar, M. a. D. Gonçalves, V.D. Pinto, R.C.S. Dias, M.R.P.F.N. Costa, R. Giudici, Mathematical Modeling of NMRP of Styrene-Divinylbenzene over the Pre- and Post-Gelation Periods Including Cyclization, Macromol. React. Eng. 8 (2014) 295–313. [43] A.J. Scott, A. Nabifar, J.C. Hernández-Ortiz, N.T. McManus, E. Vivaldo-Lima, A. Penlidis, Crosslinking nitroxide-mediated radical copolymerization of styrene with divinylbenzene, Eur. Polym. J. 51 (2014) 87–111. [44] O. Okay, D. Kaya, O. Pekcan, Free-radical crosslinking copolymerization of styrene and divinylbenzene: real time monitoring of the gel effect using fluorescence probe, Polymer 40 (1999) 6179–6187. [45] J.A. Biesenberger, D.H. Sebastian, Principles of polymerization engineering, Wiley & Sons, New York, 1983. [46] S. Beuermann, M. Buback, Rate coefficients of free-radical polymerization deduced from pulsed laser experiments, Prog. Polym. Sci. 27 (2002) 191–254. [47] T. Kothe, H. Fischer, Formation rate constants of the Mayo dimer in the autopolymerization of styrene, J. Polym. Sci. Part A Polym. Chem. 39 (2001) 4009–4013. [48] S. Marque, C. Le Mercier, P. Tordo, H. Fischer, Factors Influencing the C-O-Bond Homolysis of Trialkylhydroxylamines, Macromolecules 33 (2000) 4403–4410. [49] J. Sobek, R. Martschke, H. Fischer, Entropy control of the cross-reaction between carboncentered and nitroxide radicals, J. Am. Chem. Soc. 123 (2001) 2849–2857. [50] D.T. Gillespie, Exact Stochastic Simulation of Coupled Chemical Reactions, J. Phys. Chem. 81 (1977) 2340–2361. [51] D.T. Gillespie, Stochastic simulation of chemical kinetics., Annu. Rev. Phys. Chem. 58 (2007) 35–55. [52] M.A. Al-Harthi, J.K. Masihullah, S.H. Abbasi, J.B.P. Soares, Dynamic Monte Carlo Simulation of ATRP in a Batch Reactor, Macromol. Theory Simul. 18 (2009) 307–316. [53] M. Al-Harthi, M.J. Khan, S.H. Abbasi, J.B.P. Soares, Gradient Copolymers by ATRP in Semibatch Reactors: Dynamic Monte Carlo Simulation, Macromol. React. Eng. 3 (2009) 148– 159. [54] C. Plessis, G. Arzamendi, J.R. Leiza, H.A.S. Schoonbrood, D. Charmot, J.M. Asua, Modeling of 22

Seeded Semibatch Emulsion Polymerization of n -BA, Ind. Eng. Chem. Res. 40 (2001) 3883– 3894. [55] M.A.D. Goncalves, V.D. Pinto, R.C.S. Dias, M.P.F.N. Costa, L.G. Aguiar, R. Giudici, Gel Formation in Aqueous Suspension Nitroxide-Mediated Radical Co-Polymerization of Styrene/Divinylbenzene, Macrmol. React. Eng. 7 (2013) 155–175. [56] G. Arzamendi, C. Plessis, J.R. Leiza, J.M. Asua, Effect of the Intramolecular Chain Transfer to Polymer on PLP/SEC Experiments of Alkyl Acrylates, Macromol. Theory Simul. 12 (2003) 315–324. [57] M. Buback, M. Busch, R.A. Liimmel, Modeling of molecular weight distribution in pulsed laser free-radical homopolymerizations, Macromol. Theory Simul. 861 (1996) 845–861. [58] M. Busch, Simulation as a Tool for Feasibility Studies about PIP- SEC Experiments, Macromol. Theory Simul. 10 (2001) 262–274.

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Graphical Abstract for: Quantitative Study on the Homogeneity of Networks Synthesized by NitroxideMediated Radical Copolymerization of Styrene and Divinylbenzene

Shaghayegh Hamzehlou1, Yuri Reyes2, Jose R. Leiza1*

Highlights

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

A Monte Carlo simulation of NMRP of styrene and divinylbenzene.



The homogeneity of the polymer network was studied quantitatively.



The NMRP led to a narrower Mc distribution compared to FRP.



Average Mc evolution in NMRP is totally different from the FRP after gelation.