A Perspective on Modeling and Characterization of Transformations in

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Industrial & Engineering Chemistry Research

A perspective on modeling and characterization of transformations in the blocky nature of olefin block copolymers Mostafa Ahmadi1, Mohammad Reza Saeb2*, Yousef Mohammadi3, Mohammad Mehdi Khorasani3, and Florian J. Stadler4-7*. 1

Department of Polymer Engineering and Color Technology, Amirkabir University of Technology, Tehran, Iran.

2

Department of Resin and Additives, Institute for Color Science and Technology, P.O. Box: 16765-654, Tehran, Iran.

3

Petrochemical Research and Technology Company (NPC-rt), National Petrochemical Company (NPC), P.O. Box 14358-84711, Tehran, Iran.

4

College of Materials Science and Engineering, Shenzhen University, Shenzhen 518060, PR China

5

Shenzhen Key Laboratory of Special Functional Materials, Shenzhen 518060, PR China

6

Shenzhen Engineering Laboratory for Advanced Technology of Ceramics, Shenzhen 518060, PR China

7

Nanshan District Key Lab for Biopolymers and Safety Evaluation, Shenzhen 518060, PR China

E-mail: [email protected] (MRS), [email protected] (FJS)

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Abstract Traditional characterization methods are still unable to reveal the block structure of olefin block copolymers (OBCs). Therefore, extending the predictability of our well-developed computer code (Mohammadi et al., Macromolecules, 2014, 47, 4778-4789); the blocky nature of OBCs is modeled and characterized. The expanded model could produce diversity of macromolecules varying the concentration of chain-shuttling agent, catalyst ratio, and monomer composition, as key processing variables. The OBCs were screened and distinguished in view of chain related specifics i.e., chain length and chemical composition distribution as well as block related characteristics i.e., number, length and chemical composition of hard and soft blocks. A detailed picture of blockiness was captured and visualized tracing transitions in the microstructure of copolymers, from the case corresponding to blend copolymer (without any shuttling) to OBC (with considerable shuttling) and then to random copolymers, reflecting the significance of the chosen parameters in determining the blockiness of OBCs.

Keywords: chain shuttling polymerization, olefin block copolymer, Monte Carlo simulation, statistical analysis, processing variables


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Introduction When checking literature on polyolefins, it becomes evident how much emphasis is put into state-of-the-art and developing trends of this family of polymers in view of both industrial and academic considerations. From the 1930s onwards, engineers, and scientists alike were attempting to obtain the most favorable derivatives from olefinic monomers, thereby, shedding light on structure-property correlations in the assigned systems.1-4 After the discovery of metallocene catalysts for well-defined structures, one of the main breakthroughs in this field in the last decade was the introduction of “olefin block copolymers” (OBCs) that could afford unique architectural features and subsequently, novel properties.5,6 The innovation of “chain shuttling

polymerization”

(CSP),

in

comparison

to

conventional

ethylene/α-olefins

copolymerization with Ziegler-Natta catalysts, lies in the use of “chain shuttling agents” (CSAs), which enable the shuttling of growing chains between different active catalyst centers.5-7 The blocky nature of OBCs originates from hard crystallizable ethylene segments, at the same time, soft blocks with higher comonomer content that allow for producing copolymer chains with a new range of physical, mechanical, thermal, and rheological properties.8-16 The architectural features of OBCs such as hard block fraction, average block length, and difference in comonomer content of blocks, can be controlled in the course of CSP process by careful selection of the feeding strategy of catalyst, CSA, and monomer, respectively.5,17 Arriola et al., elaborated that attachment of more bulky ligand substitutes to the catalysts dramatically govern the ethylene selectivity, which has been evidenced by significant differences in crystalline structure of the resulting copolymers.5 Elsewhere, it was elucidated that the simultaneous activation of catalysts yields copolymers with a wide range of crystallinity and 3 ACS Paragon Plus Environment


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melting temperature due to different structures of the selected hard block catalysts.17 The idea of producing linear-hyperbranched multi-block polyethylene by using binary catalyst systems capable of gaining hyperbranched and linear segments, respectively, through chain walking and chain shuttling polymerizations, was another appealing approach examined for the tuning the microstructure by manipulation of the catalytic system.18 By changing monomer type and stereoselectivity of the catalyst, the regio- and stereospecific copolymerization of styrene, isoprene, and butadiene resulted in a novel family of stereoregulated copolymers. In this regard, block compositions and melting points could be tuned by changing feed composition.19,20 Obviously, for a given catalytic system, morphology, crystallization kinetics, mechanical properties, and rheological characteristics of OBCs are governed by architectural characteristics.8-16 For instance, it was observed that the difference between 1-octene comonomer content of the soft and hard blocks (ΔC8) strongly governs the crystallization kinetics and the degree of mesophase separation.13-15 Consequently, for a sufficiently high 1octene content difference, OBCs self-assemble into domains in the melt, giving rise to more complex quasi solid-state structures.13 Correspondingly, improved mechanical properties would be expected when OBCs crystallize from the homogeneous melts at lower temperatures.15 Elsewhere, it was shown that lower ΔC8 as well as higher CSA levels, i.e., shorter blocks, lead to increasingly random copolymers and, hence, suppress mesophase separation, as proven by rheological assessments.16 In the light of above-cited literature, achieving satisfactory properties needs to be assured by controlling the degree of blockiness and identification of transitions in the microstructure of 4 ACS Paragon Plus Environment

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synthesized copolymer chains in the course of polymerization from the case corresponding to blend to the OBC and then random copolymer. However, traditional characterization methods are still unable to reveal the block structure in OBCs made by CSP, nowadays. Correspondingly, it becomes necessary to understand and visualize transformations in copolymer microstructure at the course of CSP by considering a more comprehensive model that captures transformations in blockiness of OBCs in terms of processing parameters. In a recent work, we developed a theoretical model based on Kinetic Monte Carlo (KMC) simulation approach and monitored CSP of ethylene and 1-octene in a semibatch operation and captured contributions of chain transfer reversibility and other chain breaking reactions in controlling distribution fashion of molecular weight and chemical composition.21 Compared to simple models based on the method of moments,22,23 KMC can provide a detailed molecular level image from the microstructure of the produced chains. Through a comparative study, we have shown that the formation of dead chains through irreversible chain breaking reactions moves the coordinative chain transfer polymerization (CCTP) towards broader molar mass distributions. It was also explained that the incorporation of CSA in a dual catalytic system of CSP turns bimodal molecular weight distributions (MWD) and copolymer composition distributions (CCD) into unimodal patterns. Many architectural features including ethylene sequence length (ESL) distribution and longest ethylene sequence length (LESL) distribution-as signature of CSA performance-were also quantified in the presence and absence of hydrogen to capture an image on gradient copolymers in the CCTP and blocks with gradually changing composition in the CSP.



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In the current work, we extended the predictability of the original home-generated KMC computer code to produce in an efficient way a wide variety of OBCs with different architectural features, especially with respect to hard and soft blocks.21 Microstructural evolutions are visualized in terms of processing parameters consisting of CSA level, catalyst composition, and monomer ratio, through which a detailed perspective on the blocky nature of the growing chains is presented. The huge number of copolymer chains corresponding to different cases at which the aforementioned parameters were changed necessitated a wellmanaged data storage structure capable of capturing diverse transformations in the blocky nature of copolymers. Macromolecules born in the simulation space were characterized, screened, and stored ranging from blend copolymers with no shuttling to OBCs with considerable, as well as random copolymers with excessive shuttling reactions. The transition zones were traced in terms of microstructural features and the corresponding distributions. The ability to present an overlay plot of ΔC8 and hard block (HB) weight fraction, when catalysts composition and monomer compositions are simultaneously changed, gives the current work the potential to synthesize OBCs possessing predetermined blocky structure with the minimum undesired blend and random copolymer chains.

Model development Investigation of microstructural evolution in the olefin block polymerization media, at which catalysts with dual nature are used, was the subject of previous studies of this group.24, 25 A utilitarian KMC simulation algorithm enabled modeling of semibatch copolymerization of


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ethylene and 1-octene with a reactor size of 1011 ethylene molecules and the other reactants according to the recipe and circumstances discussed in a previous work.21 It is worth mentioning that keeping track of such a large number of molecules fed into the simulation space, along with diverse events taking place through which macromolecules are generated necessitates implementation of a professional data storage structure.26,

27

The ability to

capture and analyze fluctuations in microstructure and topological features of the simulated copolymers including MWD, CCD, ESL and LESL distributions of the OBCs as well as their corresponding distributions in the soft and hard blocks were accordingly taken into consideration. In the current work, the predictability of the original code was extended to enable tracking of microstructural evolutions including block length, content and composition in terms of the most important processing parameters in CSP consisting of CSA level, catalyst composition, and monomer ratio, to provide a perspective on the blocky nature of the growing chains. Each OBC chain in the (virtual) polymerization media contains a number of soft and hard blocks with fixed lengths and architecture (i.e., static blocks, which will not grow or reorganize anymore). Except dead chains, the terminal block on the active-side of living or dormant chains is alive (i.e., a dynamic block), which can propagate further until experiencing a cross-shuttling or termination event, turning it into a dead chain. It should be mentioned that it is also possible that shuttling transfers the dynamic block to a catalyst of the same type (homo-shuttling), which will keep the block dynamic, despite the fact that a different active center of the same type polymerizes it.



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Accordingly, a well-defined data storage structure was designed to store all topological information necessary to completely visualize an OBC chain. The strengthened algorithm, implemented in this work, enables to store all instantaneous characteristics of dynamic last block along with all cumulative information of static blocks on the same chain. This algorithm allowed the simulation of a statistically very huge sample size with a computationally costeffective execution time. Executing a simulation with this program, in total consumes around 10 hours of calculation time on a desktop computer with Intel Core i7-3770K (3.50 GHz), 32 GB of memory (2133 MHz) running on Windows 7 Ultimate21. Three independent adjustable process parameters-namely CSA level, catalyst composition, and monomer molar ratio, were selected. The CSA level was defined as the logarithm of CSA concentration divided by the original CSA concentration of 0.27 g/L used in former theoretical works.21-23 On the other hand, molar fraction of Catalyst 1 responsible for producing soft block (by our definition) and molar fraction of ethylene in the monomer feed were altered. Accordingly, the mentioned parameters were varied in the ranges from -3 to -1 in log scale, from 0.2 to 0.8, and from 0.2 to 0.8, respectively, to evaluate the sensitivity of microstructural features on the chosen varied parameters. The preference of semi-batch processes over continuous copolymerization, regardless of the mild composition drift unavoidable in the former, was chosen due to the possibility to obtaining microstructural features possessing narrower distribution patterns, as it was proven that such distributions were widened in continuous copolymerizations as a consequence of residence time distribution.5


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Results and discussion Expedition of microstructure land by means of KMC To illustrate the reliability of the developed KMC code in predicting the evolutionary events taking place at the course of copolymerization, we first evaluated the simultaneous effects of the catalyst composition and CSA level on some well-known features, i.e., degree of polymerization and number of blocks in OBC chains. As can be seen in Figure 1a, increase of CSA level causes production of short copolymer chains, regardless of catalyst composition, as a result of increase in the number of existing chains and excessive chain transfer reaction. Further, when the catalyst system is mainly composed of homopropagation catalyst responsible for production of hard blocks, longer copolymers are synthesized, due to lower tendency to irreversible transfer to hydrogen. Nevertheless, at high CSA levels this effect is weakened by dominance of reversible transfer to CSA. Likewise, increasing the CSA level yielded more blocks due to domination of chain shuttling reactions (see Figure 1b, for sake of presentation clarity CSA-axes is inverted). Noticeably, in the vicinity of 50% catalyst composition, at high CSA levels, the number of blocks experiences a maximum as a result of domination of cross-shuttling over homo-shuttling reaction.



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Figure 1. The effect of catalyst composition and CSA level on the degree of polymerization (a) and number of blocks (b) of OBC chains, at monomer composition of 0.6.

To identify the blocky nature of OBCs, the copolymer chains born in the simulation space were screened in terms of block length and the three-dimensional figures were plotted for soft and hard blocks, separately (Figure 2).

Figure 2. The effect of catalyst composition and CSA level on the length of soft (a) and hard (b) blocks, at monomer composition of 0.6.


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In agreement with changes in the polymerization degree (Figure 1a), the higher the CSA level the lower is the block length. Moreover, the imbalance in the catalyst composition towards each catalyst increases the corresponding block length due to the governance of homoshuttling. The length of soft blocks levels off at low CSA levels as shown in Figure 1a, since irreversible transfer to hydrogen takes the control of fixing block length after a critical CSA concentration. Dissimilarly, the length of hard blocks even exceeds the average degree of polymerization in this region, which seems quite peculiar at the first glance. Nevertheless, at such low CSA-levels, the likeliness of producing chains without any blocks is indeed high, so that the result is a blend composed of soft and hard chains. Considering the fact that homopolymerization of ethylenic hard units will overtake copolymerization with 1-octene, and hard block catalyst has lower tendency to chain transfer to hydrogen, such behavior can be explained. This transitional behavior is consistent with formation of chains having one block on average, as visualized in Figure 1b. On the basis of the above discussions, it could be interesting to categorize copolymer chains based on their blocky state. In this regard, three different regions could be identified and distinguished based on CSA level, as (I) copolymer blend, (II) OBC, and (III) random copolymer. Figure 3 provides qualitative circumstances to distinguish transitions in the blocky nature of the produced copolymers. At high CSA levels, the rapid shuttling reaction may make so short blocks that the average ethylene sequence length (ESL) would be undistinguishable between hard and soft blocks. In other words, the ratio of ESL in hard to soft blocks approaches unity and a random copolymer is effectively formed, as depicted in Figure 3a. Again the bias in the catalyst composition towards each catalyst increases the corresponding ESL due to the profound homo11 ACS Paragon Plus Environment


shuttling. On the other hand, at low CSA levels copolymer chains might be formed independently by each of the catalysts without any shuttling reaction. In this regime chains with distinguishable microstructure are specific signatures of each corresponding catalyst. Difference in CCD is one of the key factors in determining the capabilities of catalysts used in CSP. As depicted in Figure 3b, a blend composed of chains with significantly different CCDs are produced at low CSA levels. The bimodal distribution vanishes at higher CSA levels and turns into a narrow peak at higher CSA levels. Similar behavior could be obtained in tracing MWD development as a function of CSA level,23 however the difference is more profound in CCD.

(b) CSA1 CSA0 CSA-1 CSA-2 CSA-3

0.3

Weight percent (%)

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0.2

0.1

0.0 0

3

6

9

12

15

18

Comonomer content (mol%)

Figure 3. Microstructure evolution as a result of changing CSA level, (a) ESL of hard divided by soft blocks at monomer composition of 0.6 and (b) CCD as a function of CSA level at constant catalyst composition 0.4 and monomer molar ratio of 0.6 (data smoothed by percentile filter).

The studied simulation runs highlighted the importance of selecting suitable CSA level for production of pure OBC chains and avoiding undesired formation of polymer blends or random 12 ACS Paragon Plus Environment

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copolymers, which is a prerequisite for studying the effects of reaction parameters on microstructure and properties of the produced blocky copolymers. Figure 4 displays some useful information on the dependence of key microstructural characteristics on the processing variables at a constant CSA level that assures production of OBCs with the minimum possibility of formation of blends or random copolymers. The difference in the comonomer content of hard and soft blocks determines the degree and somehow the kinetics of micro-phase separation, which in turn affects the crystallization behavior and the rheological properties at low frequencies.8-16 This parameter designated as ΔC8 could be directly tuned by variation of catalyst and monomer feed composition as depicted in Figure 4a. The main influential process parameter in controlling ΔC8 is monomer composition; in a manner that ΔC8 would be enlarged at higher α-olefin comonomer levels. The weight percentage of hard blocks directly affects the crystallinity of OBC and consequently the mechanical properties9-11,28 and also the rheological properties.16 Higher modulus and stress at break and lower strain at break are expected in tensile behavior of OBCs with higher fractions of hard blocks.9-11 While the length of hard and soft blocks could be tuned by controlling CSA level, their corresponding overall fraction could be directly tailored through catalyst composition as given in Figure 4b. Homo-shuttling to the more abundant catalyst species would lengthen the corresponding block and, consequently, its weight fraction, consistently. It is worth mentioning, opposed to the expectations, increasing comonomer content in the feed peculiarly increases total fraction of hard blocks (to a minor extent as can be seen in Figure 4b), as the chance of fast homo-propagation in soft blocks would be reduced more significantly than in hard blocks. 13 ACS Paragon Plus Environment


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Lastly, the average longest ethylene sequence (LES) responsible for precipitation temperature of copolymers from solution29 can be likewise regulated by adjusting monomer feed composition (Figure 4a), so that increasing ethylene fraction results in higher LES. At high ethylene ratios, however, LES would be interrupted due to dominance of cross-shuttling reactions at intermediate catalyst compositions, as depicted in Figure 4c.

Figure 4. The effects of catalyst and monomer feed compositions on (a) the difference of comonomer content in hard and soft blocks, (b) weight fraction of hard blocks, and (c) LES of OBCs at CSA level of 0.


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The described examples qualitatively determined the extremes and characteristics of microstructures that assists process engineers to ascertain whether the targeted OBC can be produced when concentrations of CSA, monomers and catalysts are changed in the studied variation interval. The exact tailoring of the microstructure, however, needs further knowledge on quantitative guidelines towards tuning multiple microstructure characteristics in such a complex multi-variable process. While this information could not be easily provided by performing synthesis experiments due to an overwhelming number of syntheses and characterizations, thanks to the detailed mechanistic KMC model developed in our recent works we can draw quantitative instructions for synthesis of desired OBCs with comparatively small time effort. In the next section, we describe statistical correlations between independent process variables and dependent OBC features and used them for designing an OBC with specific microstructural features as an example.

Designing favorable OBC Diverse aspects of microstructure characteristics of OBCs and transformations in their blocky structure upon alterations in process parameters were investigated in the former section. Here we use the wealth of data provided by KMC on details of blocky nature of OBCs to statistically examine the significance of correlations between process variables and key microstructural features. Table 1 presents statistical correlation analysis between the aforementioned parameters based on Pearson Product Moment (PPM) and P-value. PPM varies between -1 and +1 measures the strength of direct or inverse relationship between each pair of variables, respectively. The most independent variables should have zero PPM. Likewise, P-values below 15 ACS Paragon Plus Environment


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0.05 indicate statistically significant correlations at the 95% confidence level. For ease of reading, the significant correlations are highlighted by bold values.


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Table 1. Statistical correlation analysis process variables and key microstructural characteristics Variable

Criterion

ΔC8

HB (wt%)

LES

Monomer composition

PPM

-0.9384

0.0006

0.6324

P-Value

0.0000

0.9965

0.0000

PPM

0.0206

-0.9570

-0.4683

P-Value

0.8705

0.0000

0.0001

PPM

-0.1171

0.0087

-0.3315

P-Value

0.3528

0.9451

0.0070

Catalyst composition

CSA level

As graphically demonstrated in the previous section, ΔC8 and weight fraction of hard blocks can be tuned by adjusting monomer and catalyst compositions, respectively, while LES is affected by both process parameters with lower statistical significance. A similar conclusion could be drawn based on the statistical criteria provided in Table 1. Multivariable regression analysis was performed to quantify the relationships between the process parameters and the mentioned OBC characteristics. Table 2 lists the fitted constants to the equation with the following general formula, and the corresponding R² measure of regression predictability. = + . + . (1)



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Table 2. Multivariable regression equation’s constants OBC feature Regression method

A

B

C

R2

ΔC8

Multivariable

57.89 -74.09

ΔC8

Single variable

51.69 -71.55

HB (wt%)

Multivariable

73.94 -18.20

-77.06 95.21

HB (wt%)

Single variable

64.70

-74.10 91.58

LES

Multivariable

79.13 769.08 405.39 52.32

-

-10.71 90.83 -

88.06

The statistically relevant pair of variables could be satisfactorily correlated by single variable regression method. However, multivariable regression equations were used for the optimization purpose. The master-curve (Figure 5) demonstrates an example of multi-objective optimization of process parameters including monomer and catalyst compositions in order to attain OBCs possessing ΔC8 in the arbitrary range of 20 to 30% and hard block’s weight fraction in the limits of 10 to 20%. Such overlay plots give an overview of developments in the microstructure-property correlations and can be taken for careful selection of determining parameters to achieve OBCs with predetermined characteristics.


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0.8

0.7

Catalyst composition (mol%)

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0.6

0.5

0.4

∆C8= 20 ∆C8= 30 HB(wt%)= 10 HB(wt%)= 20

0.3

0.2 0.2

0.3

0.4

0.5

0.6

0.7

0.8

Monomer composition (mol%)

Figure 5. Simultaneous optimization of process variables (monomer and catalyst compositions) to meet the desired microstructural properties (20

A Perspective on Modeling and Characterization of Transformations in

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