doi.org/10.26434/chemrxiv.6406886.v1

The Effect of Tacticity and Side Chain Structure on the Coil Dimensionsof PolyolefinsMohammad Atif Faiz Afzal, Jarod M. Younker, George Rodriguez

Submitted date: 04/06/2018 • Posted date: 05/06/2018Licence: CC BY-NC-ND 4.0Citation information: Afzal, Mohammad Atif Faiz; Younker, Jarod M.; Rodriguez, George (2018): The Effect ofTacticity and Side Chain Structure on the Coil Dimensions of Polyolefins. ChemRxiv. Preprint.

The key to the discovery of materials with targeted properties lies in the understanding of structure-propertyrelationships. In this work, we evaluate the relationship between the polymer structure and their coildimensions, and explore new polymers based on these relations. Coil dimensions are important features ofpolymers which affect their performance in various applications, including drug delivery, waste-watertreatment, and engine oils. Coil dimensions of the polyolefins are dependent on the number, size, and stereoorientation of side chains along the backbone. Thus, controlling these attributes allows us to tailor the coildimensions of polyolefins. In the proposed scheme, we calculate the radius of gyration (Rg) of polyolefinchains using molecular dynamics simulations and validate against experimental results. Simulated annealingis implemented to ensure the capture of different configurations. This model affords the ability to quantify theeffect tacticity has on the coil dimensions of polyolefins. The results show the suppression of tacticity effectswhen the polymer chains transition to bottlebrush structures, demonstrating that the side chain sterichindrance plays an important role in the rigidity of the chain backbone. Further, the model is used to evaluatethe compositional effects by determining the rigidity of propylene and 1-hexene copolymers. Combining ourmodel with virtual high-throughput screening techniques, we evaluated the coiling behavior of hundreds ofnew polymers. Using the screening results, we established correlations between the structure of the sidechain and the coil dimensions of polymers.The supplementary material accompanying this paper includes thelibrary of 275 polymers and their corresponding Ks values.

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http://doi.org/10.26434/chemrxiv.6406886.v1https://chemrxiv.org/authors/Mohammad_Atif_Faiz_Afzal/4455793https://chemrxiv.org/ndownloader/files/11830712https://chemrxiv.org/articles/The_Effect_of_Tacticity_and_Side_Chain_Structure_on_the_Coil_Dimensions_of_Polyolefins/6406886/1?file=11830712https://chemrxiv.org/ndownloader/files/11830715https://chemrxiv.org/articles/The_Effect_of_Tacticity_and_Side_Chain_Structure_on_the_Coil_Dimensions_of_Polyolefins/6406886/1?file=11830715

The effect of tacticity and side chain structure on the coil dimensions of polyolefins

Mohammad Atif Faiz Afzal,1, 2, ∗ Jarod M. Younker,2, † and George Rodriguez2, ‡

1Department of Chemical and Biological Engineering, University at Buffalo,The State University of New York, Buffalo, NY 14260, United States

2ExxonMobil Chemical Company, Baytown Technology and Engineering Complex, Baytown, Texas 77520, United States(Dated: June 1, 2018)

The key to the discovery of materials with targeted properties lies in the understanding ofstructure-property relationships. In this work, we evaluate the relationship between the polymerstructure and their coil dimensions, and explore new polymers based on these relations. Coil di-mensions are important features of polymers which affect their performance in various applications,including drug delivery, waste-water treatment, and engine oils. Coil dimensions of the polyolefinsare dependent on the number, size, and stereo orientation of side chains along the backbone. Thus,controlling these attributes allows us to tailor the coil dimensions of polyolefins. In the proposedscheme, we calculate the radius of gyration (Rg) of polyolefin chains using molecular dynamics sim-ulations and validate against experimental results. Simulated annealing is implemented to ensurethe capture of different configurations. This model affords the ability to quantify the effect tacticityhas on the coil dimensions of polyolefins. The results show the suppression of tacticity effects whenthe polymer chains transition to bottlebrush structures, demonstrating that the side chain sterichindrance plays an important role in the rigidity of the chain backbone. Further, the model isused to evaluate the compositional effects by determining the rigidity of propylene and 1-hexenecopolymers. Combining our model with virtual high-throughput screening techniques, we evalu-ated the coiling behavior of hundreds of new polymers. Using the screening results, we establishedcorrelations between the structure of the side chain and the coil dimensions of polymers.

Keywords: radius of gyration; coil dimension; tacticity; polyolefins; molecular modeling; high-throughputscreening; molecular library

I. INTRODUCTION

The development of new polymeric materials with de-sirable properties often hinges on an understanding ofstructure-property relationships. The relevant materialproperties necessary for building these relationships areeasily identified within the context of the problem be-ing investigated. By contrast, determining the impor-tant structural attributes often represents a greater chal-lenge. One of the main reasons for this difficulty is thatpolymer structures may be defined through a myriad ofmolecular attributes including composition, topology orconnectivity, molecular weights, distributions and modal-ities [1]. The number and size of side-branches also con-tribute to physical properties [2]. Exacerbating the situ-ation even further is the effects the stereo orientation ofbranched moieties along the polymer backbone have onmaterial performance properties. Often the effect is notso subtle. In fact, stereoregularity or tacticity of poly-olefins is known to significantly impact the physical prop-erties of polymer melts and solutions [3–5]. Tacticity mayalso play a commonly underestimated role in connectionwith coil dimensions [6]. A good illustration of this phe-nomenon was described by Sun and co-workers [7] whoshowed how syndiotactic polypropylene at a fixed molec-ular weight has a higher radius of gyration (Rg) com-

∗ m27@buffalo.edu† jarod.m.younker@exxonmobil.com‡ george.rodriguez@exxonmobil.com

pared to an isotactic analog. A similar trend is observedfor the intrinsic viscosity of polyolefins, i.e. syndiotacticpolyolefins have higher intrinsic viscosity compared totheir isotactic analogs. Therefore, controlling the stere-oregularity is important for controlling the coil dimen-sions of these polymers. The inclusion of comonomersalso impacts the Rg of the resulting copolymers [8]. Un-derstanding the fundamental physics of these systems isvital for their development. For example, it is believedthat tacticity and composition are important features af-fording control over attributes affecting the performanceproperties of viscosity modifiers (VMs) [6, 9]. In additionto VMs, these attributes of polymers are key parame-ters in various other applications, such as drug delivery,waste-water treatment, construction material, medicine,etc. [10–12].

Upon identifying structural characteristics necessaryfor creating useful structure-property relationships, thenext step is to select an approach to quantify these fea-tures. Synthesis and experimental testing of new poly-mers are resource intensive, and therefore limit the scopeof exploring new polymer candidates. Progress in the dis-covery of new materials is increasingly driven by the useof computational tools [13, 14]. One of the prerequisitesof a computational approach for materials discovery isaccess to models which accurately predict target proper-ties or proxies thereof [15]. By developing in silico mod-els which predict polymer attributes accurately, we canmore quickly and efficiently identify promising polymersystems if these attributes relate well to applications ofinterest. For example, a model to estimate polymer coil

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dimensions of stereoregular poly α-olefins would be ofgreat value in an industrial environment, as these poly-mers should provide a basis for understanding and devel-oping novel VMs. It is well known that the VMs play akey role in the fuel economy (FE) of vehicles [16, 17]. Var-ious polymers such as olefin copolymers, styrenic blockcopolymers and poly alkyl methacrylates have been usedas VMs [18–20]. Improving the FE is increasingly impor-tant for creating next-generation olefin copolymer basedVMs. Prior attempts to improve VM performance haverelied heavily on a range of synthetic manipulations [21–24]. However, the underlying physics dominating theproperties and subsequent performance of these systemsremains comparatively unexplored and therefore less un-derstood. Models could guide and speed experimental ef-forts by providing deeper insights into polymer viscomet-ric properties which are significantly faster to access thanempirical observations. At minimum, such models couldcomplement laboratory efforts leading to more completeresearch workflows which would inevitably increase thelikelihood of gaining significantly broader insights.

The Mark-Houwink equation (eq. I.1) is a relationshipbetween polymer intrinsic viscosity ([η]) and molecularweight (Mw) [25]. Equation I.2 represents a similar re-lationship between the Rg and Mw which is obtainedfrom Renormalization Group Theory [26]. These equa-tions suggest that an increase in Rg is a good indicator ofan increase in the [η] of polymers in good solvents. Thehigh computational cost of calculating polymer solutionviscosities encouraged us to focus on the comparativelymore accessible Rg which is also easily validated experi-mentally.

[η] = Kv × (Mw)αv (I.1)Rg = Ks × (Mw)αs (I.2)

Herein we present a computational approach to eval-uate the coil dimension of olefin polymers in dilute so-lutions of 1,2,4-trichlorobenzene. The approach involvescomputing the radius of gyration of polymers in solutionusing molecular dynamics. A similar approach has re-cently been implemented to evaluate the Rg of polymersin solution [27]. However, the model was not validatedagainst experimental results and did not include extrap-olation schemes for high Mw polymers. The current con-tribution introduces a robust model that includes simu-lated annealing to evaluate the Rg of polymers. Usingthis relationship, the Rg of high Mw polymers are esti-mated. The model’s accuracy is demonstrated by validat-ing with the experimental results of polypropylene (PP),poly-1-butene (P1But), poly-1-hexene (P1Hex) and poly-1-octene (P1Oct). Additionally, we provide detailed in-sights into the dependence of Rg on the tacticity and thenature of the side chain structure.

II. BACKGROUND AND METHODS

A. Polymer selection

We selected PP, P1But, P1Hex and P1Oct with differ-ent tacticities as representative homopolyolefins to val-idate our method. This choice allows us to assess theeffect monomer type and stereoregularity have on therigidity of the polymer’s backbone. The tacticity of thepolymer is indicated with letters in front of the poly-mer abbreviation (i, a, or s). The letters i, a ands represent isotactic, atactic and syndiotactic, respec-tively. For example, iPP refers to isotactic polypropy-lene. The PP chains used in this study consisted of20, 40, 60 and 80 monomers; P1But chains consist of15, 30, 45 and 60 monomers. The chains consist of10, 20, 30 and 40 monomers in all other cases. 1,2,4-trichlorobenzene(TCB) is used as the solvent to facilitatevalidation relative to available experimental results.

B. Molecular modeling

The massively parallel simulator LAMMPS was usedto carry out the molecular dynamics procedure [28]. Theinitial structures and simulation boxes were generatedwith Materials Studio 2017 R2 by BioVia [29]. In eachsimulation, the cell is first filled with the polymer chainbefore populating with the TCB molecules. In these sim-ulations, it is important to add a sufficient number ofTCBs in each simulation box so that the polymer chainsfollow the minimum-image convention. Based on this cri-teria, we added 100, 246, 417 and 606 TCBs for 20, 40,60, and 80 monomer chains, respectively. The same num-ber of TCBs were used for all polymers studied in thiscontribution. The simulation cells were built using theamorphous builder tool in Materials Studio. The energyof the cells was initially minimized using PCFF forcefieldat 450K with a target density of 0.8 g/cm3. The struc-tures were exported to MSI files and subsequently con-verted to LAMMPS files containing the OPLSAA force-field parameters using the MSI2LMP tool.

C. Simulated annealing and Rg calculation

The systems were initially equilibrated at a higher tem-perature before cooling to the temperature of interest(see Fig. 1a). The one-step annealing method will workwell for high temperatures, but might fail for low temper-ature simulations, as there is a high probability of gettingtrapped in a local minima. To prevent the entrapment,we applied simulated annealing (SA), i.e. four cycles fromhigher temperature to lower temperature. The applica-tion of SA increases our model’s robustness, as it capturesdifferent polymer configurations which are otherwise notpossible with a single temperature cycle, especially at

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lower temperatures. At every SA cycle, an NPT simu-lation was performed at the temperature of interest andheld for longer times to record Rg values as shown inFig. 1b. The following SA procedure was performed. (1)equilibrate the system at a higher temperature of 473K(2) anneal the system to 408K for 200 ps (3) equilibratethe system at 408K for 200 ps (4) hold the system at408K for 3 ns while recording the Rg of polymer at every0.1 ps interval (5) heat the system to 473K for 200ps (6)repeat the process from step 1.

The Rg of a polymer is defined as the mass averagedroot mean squared distances of all atoms from the centerof mass of the polymer as shown in eq. II.1, where miis the mass of atom i, ri is the position of atom i,rcom isthe position of center of mass of the molecule, and M isthe total mass of the molecule.

Rg =

√1

M

∑i

mi(ri − rcom)2 (II.1)

Once the Rg values for different oligomers were ob-tained, the data was fit to equation I.2 to compute theKs value of the corresponding polymer. The value of αsin the equation is a constant which depends on the sol-vent type. Empirical studies afford the αs value of 0.58for TCB [7]. A weighted least squares was performed byfitting the values of Rg and Mw to obtain the Ks valuesusing the curve fit function of the SciPy module. Theinverse values of the deviation in Rg were used as corre-sponding weights for the weighted least squares fitting.

D. Library generation and virtual high-throughputscreening

A library of α-olefin monomers (both linear and non-linear) was created using the molecular library generatorpackage, ChemLG [30]. The library was built by link-ing saturated carbon atoms in a combinatorial fashion.We used methane, ethane, and butane as the buildingblocks while considering all the hydrogens in the build-ing blocks as connection sites. The maximum number ofcarbons was restricted to twelve. Using these rules, the li-brary was built until three generations, which resulted in275 monomer structures. These monomers were used tobuild corresponding oligomers and subsequently screenedthem in a virtual high-throughput fashion to evaluatetheir chain size. We follow the process described in sec-tion 2.2 and 2.3 to calculate the corresponding Rg andKs values of these 275 polymers.

III. RESULTS AND DISCUSSION

A. Model validation

Using the aforementioned SA procedure, we calculatedthe Rg of all the polymers. The Rg variation of iPP with

time and the distribution of Rg are shown in Fig. 2a andFig. 2b, respectively. It should be noted that the systemswere in equilibrium when the Rg values were recorded.The equilibration was confirmed by checking the conver-gence of the total energy of the system. Fig. 2a suggeststhat the Rg fluctuates with time, and these fluctuationsincrease with chain size. Although these fluctuations re-sult in large deviations of Rg values, the mean value ofRg increases with the number of monomers as depictedin Fig. 2b. The spread of Rg for 20 monomers is sig-nificantly less than the spread of Rg in the 80 monomerchains, suggesting that longer chains will typically havea larger spread of Rg.

The mean Rg and the deviation of Rg for all poly-mers were evaluated and plotted against the number ofmonomers. Fig. 3a and Fig. 3b show the Rg of PP andP1Hex, respectively. The Rg values for all the polymersincrease with the number of monomers. Although sta-tistically equivalent in most cases, there is an increasingtrend with the number of monomers. More interestingly,the Rg is clearly dependent on the tacticity of the poly-mers, as the Rg increases with change in tacticity for bothPP and P1Hex. Fig. 4 presents the coil structures of PPand P1Hex obtained from the simulation, which qual-itatively shows that the syndiotactic chains have largersize compared to isotactic chains. The trajectories of iPPand sPP are included in the supplementary informationof this paper. These show the differences in relative sizes.This observation is in good agreement with the experi-mental results [7]. Note that the experimental values areavailable for high Mw polymers (10

4-106), whereas thesimulations are performed for low Mw polymers (900-4500). However, the simulation results show that thetrends in Rg for low Mw polymers are similar to thoseof high Mw polymers. This finding suggests that thesimulations can be performed on low Mw polymers andsubsequently extrapolated to obtain Rg values of highMw polymers, or at least use the simulated results as aproxy for the backbone rigidity of the larger systems.

Although there is a non-linear relationship betweenMw and Rg, the value of Ks can be used to rank thepolymers, i.e. polymers with higher Ks will exhibit highRg values at a particular Mw. The calculated valuesof Ks for PP and P1Hex are shown in Table I. Thesevalues are nominally lower than the reported experimen-tal values, but there is a clear relationship between thecalculated and experimental results. The lower Ks val-ues may hinge on the assumption that the small chainoligomers follow the same power law (αs=0.58) as thelong chain polymers. Previous studies report that vari-ous polymers in good solvents follow a lower power law forintrinsic viscosity for small molecular weight chains [31–33]. An αs value of 0.58 was used because experimentalvalues for low molecular weight polyolefin were not avail-able. In spite of this assumption, the trend in the Ksvalues was reproduced. Exact Ks values were obtainedby developing a calibration scheme. We then evaluatedthe calibration scheme with a linear regression using the

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FIG. 1. Schematic of temperature cycles used (a) one-step temperature cycle, (b) multiple temperature cycles (simulatedannealing).

FIG. 2. (a) Variation of Rg of iPP with time; (b) Histograms showing the distribution of iPP configurations.

eight experimental Ks values (see Fig. 5) which allow forthe calculations of calibrated Ks values reported in Ta-ble I. Using the calibrated Ks values in the equation I.2,Rg values of larger Mw polymers were calculated. Ourextrapolation and calibration scheme are in good agree-ment with experimental results, which is confirmed bycomparing with the experimental Rg values for high MwiPP, sPP, iP1Oct and sP1Oct (see Fig. 6).

B. Tacticity effects and bottlebrush transitionpoint

Having developed a tool to rank the coil size of poly-mers, we are able to evaluate analogous attributes ofpolymers for which we do not have experimental data. Inthis connection, the Ks values of poly-1-decene (P1Dec)and poly-1-dodecene (P1Dodec) in both isotactic andsyndiotactic forms were evaluated (Table 1). The Ksvalues for isotactic and syndiotactic polyolefins decreasewith the number of carbons in the monomer. This de-crease is substantial in the syndiotactic polyolefins com-pared to isotactic polyolefins (see Fig. 8). The effect oftacticity is significant for smaller monomers, and becomesless pronounced with the larger analogs. For example,the dimensions of iP1Dodec and sP1Dodec are indistin-guishable as suggested qualitatively by Fig. 7. The datafurther implies that α-olefins larger or equal to 1-octene

may afford polymers structures akin to bottlebrush [34].The conclusion is that the subtle tacticity effect describedabove is simply overwhelmed by the sterics of the sidechain if these moieties are large enough.

The above success in ranking isotactic and syndiotac-tic polyolefins coil dimensions lends credence to the pro-posed scheme, and encouraged us to explore the tool’sfidelity. We evaluated the dependency of Ks on tacticityby tracking the Ks of PP chains as the stereoregularitywas changed from isotactic to syndiotactic by calculat-ing the individual Ks values using the Rg values of PPoligomers containing 20, 40 and 60 monomer units. Theresults of this progression are depicted in Fig. 9, andrepresent the expansion of the points in Fig. 3a. In thisfigure, 0% tacticity refers to iPP, 50% tacticity refersto aPP, and 100% tacticity refers to sPP. The Ks valueof PP chains increases with the tacticity. This resultsuggests the model’s fidelity is moderate in ranking coildimensions of polypropylene, yet useful in differentiat-ing the isotactic and syntiotactic analogs. Understand-ing compositional space may be accomplished by addingcomonomers to PP. Accordingly, the effect comonomershave on the Rg of homopolypropylene were evaluated.

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FIG. 3. Variation of Rg with increasing number of monomers: (a) for PP and (b) for P1Hex.

FIG. 4. Snapshots extracted from the MD trajectory of: (a) iPP, (b) sPP, (c) iP1Hex, and (d) sP1Hex.

C. Effect of polymer composition

Syndiotactic polypropylene has the largest coil dimen-sions among poly α-olefins. However, the crystallinity ofsPP limits its use in various applications [35, 36]. Incor-porating larger comonomers (e.g., 1-butene, 1-pentene,1-hexene, 4-methyl-1-pentene)[37, 38] allows us to ad-dress this limitation. The crystallization behavior ofthese copolymers is well studied, but the effect of suchcompositions on the coil dimensions is not as well un-derstood. We therefore evaluated the coil dimensions ofpropene and 1-hexene copolymers. Eleven copolymerswere created from propene and 1-hexene by increasing 1-hexene content from 0 wt% to 100 wt%, and subsequentlycalculating their Ks values. Figure. 10 shows the effectof comonomer on Ks, and suggests that polypropylene

with 20 wt% 1-hexene retains the benefits of syndiotac-ticity. It should be noted that the copolymer chains wererandomly generated. To confirm that the calculated Ksvalues are not biased on a single random sampling, tenrandom samples were tested for the 20 wt% 1-hexenecopolymer and 95 wt% 1-hexene copolymer. The meanKs values for the ten samples of the 20 wt% copoly-mer and 95wt% copolymer is 2.09×10−2(±0.05) nm and1.57×10−2(±0.04) nm, respectively. These results indi-cate that the effect of random sampling is minimal inobtaining the dependence of composition on the coil di-mensions of copolymers.

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TABLE I. Comparison of the calculated and experimental Ks values of polyolefins.

Polymer AbbreviationKs × 102nm(exp.) [7]

Ks × 102nm(calc.)

Ks × 102nm(calc.) calibrated

Isotactic polypropylene iPP 1.73 1.49 ± 0.12 1.70 ± 0.13Syndiotactic polypropylene sPP 1.99 1.98 ± 0.15 2.12 ± 0.17Isotactic poly-1-butene iP1But 1.52 1.29 ± 0.04 1.53 ± 0.05Syndiotactic poly-1-butene sP1But 1.74 1.53 ± 0.10 1.73 ± 0.11Isotactic poly-1-hexene iP1Hex 1.44 1.20 ± 0.05 1.45 ± 0.05Syndiotactic poly-1-hexene sP1Hex 1.56 1.32 ± 0.06 1.56 ± 0.07Isotactic poly-1-octene iP1Oct 1.38 1.13 ± 0.03 1.40 ± 0.04Syndiotactic poly-1-octene sP1Oct 1.44 1.20 ± 0.05 1.45 ± 0.06Isotactic poly-1-decene iP1Dec - 1.12 ± 0.04 1.38 ± 0.05Syndiotactic poly-1-decene sP1Dec - 1.17 ± 0.04 1.43 ± 0.05Isotactic poly-1-dodecene iP1Dodec - 1.10 ± 0.03 1.36 ± 0.03Syndiotactic poly-1-dodecene sP1Dodec - 1.14 ± 0.04 1.40 ± 0.05Atactic polypropylene aPP - 1.72 ± 0.13 1.90 ± 0.15Atactic poly-1-hexene aP1Hex - 1.27 ± 0.05 1.51 ± 0.06Isotactic poly-4-methyl-pentene iP4MP - 1.16 ± 0.04 1.42 ± 0.05Syndiotactic poly-4-methyl-pentene sP4MP - 1.43 ± 0.05 1.65 ± 0.06Isotactic polyvinyl cyclo-hexane iPCycHex - 1.10 ± 0.01 1.36 ± 0.02Syndiotactic polyvinyl cyclo-hexane sPCycHex - 1.20 ± 0.02 1.45 ± 0.02

FIG. 5. Comparison of the calculated Ks vs experimental Ksvalues.

D. Effect of side chain structure

In addition to linear α-olefin polymers, the Ks valuesof two non-linear α-olefin polymers were calculated: poly4-methyl-1-pentene (P4MP) and polyvinyl cyclo-hexane(PCycHex). The data in table I shows that sP4MP hasa higher Ks than sP1Hex. On the other hand, the Ks ofsPCycHex is significantly lower than that of sP1Hex. Wecompare P1Hex with PCycHex, as their side chain exten-sion from the backbone are similar. However, the cyclicring affords a stiffer moiety. These comparisons illustrate

FIG. 6. Comparison of the calculated and experimental Rgvalues for sPP, iPP, sP1Oct and iP1Oct. The light coloredarea represents the standard deviation of the calculated Rgvalues.

that a slight change in the side chain structure may resultin alterations of polymer coil dimensions. Changing themonomer from 1-hexene to 4-methyl-1-pentene providesa more flexible backbone as indicated by the resultingKs value (see Fig. 11); while a more rigid backbone isobtained when the 1-hexene monomer is replaced withvinyl cyclo-hexane. Additionally, the difference in theKs values of syndiotactic and isotactic conformations,∆(Ks)(i→s), of these polymers indicates that the coil

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FIG. 7. Snapshots extracted from the MD trajectory of: (a) iP1Dodec, and (b) sP1Dodec.

FIG. 8. Variation of Ks values with increase in the numberof carbons in the monomer. The light colored area representsthe standard deviation of the calculated Ks values.

FIG. 9. Variation in the Ks values with an increase in tacticityof PP chains.

FIG. 10. Variation in the Ks values with hexene content inthe copolymer of propene and 1-hexene.

size of flexible polymers is dependent on their tacticity.For example, the flexible polymer sP4MP has a larger∆(Ks)(i→s) value than the less flexible sP1Hex. This re-sult further corroborates our earlier hypothesis describedin section III B.

E. Optimizing the side chain structure via virtualhigh-throughput screening

Findings from section III D suggest that the steric hin-drance of the side chain is crucial to the polymer coildimension. Therefore, the polymer backbone rigiditycan be tuned by tailoring the side chain structure. Moststructural explorations are often based on intuition, andare typically limited by resource availability. On theother hand, using the methodology described above, wecan study the coil dimensions of large number of poly-mers. This motivated the generation of a virtual libraryof many possible structures for the side chain. Large

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FIG. 11. Comparison of the coil dimensions of sPH, sP4MP,and sPCH.

scale exploration of the side chain structure will not onlyprovide a greater diversity of structures for specific ap-plications, but will also allow us to determine underlyingstructure-property relationship of novel systems.

A library of 275 monomer structures was generatedusing the method described in section II D. We then cre-ated oligomers containing 10, 20, 30, and 40 monomerunits for each of these polymers and subsequently per-formed MD simulations. Using the Rg values obtainedfrom MD simulations, the Ks values were calculated forall the 275 species. The structure of these monomersand their corresponding Ks values are included in thesupplementary information. From the distribution ofthe Ks values (see Fig. 12), it is noted that the val-ues range from 1.0x10−2nm to 2.1x10−2nm, with ma-jority of the polymers having a value of 1.3x10−2nm.The two polymers which have the highest Ks values arepolypropylene and poly-1-butene. To further develop theunderlying structure-property relationship, the Rg of theside chains (Rgsc) were calculated using the optimizedmonomer structure and correlated with the correspond-ing polymer Ks values (see Fig. 13). The Ks values de-crease with Rgsc until 2.5 nm and become independentthereafter.Rgsc value gives a quantification for the size of the

side chain, however, it does not represent the shape. Toinclude the effect of shape, a new parameter is defined–Bulkiness factor (Bsc). This parameter is the product ofRgsc and the distance between the beta carbon and theside chain center of mass, Dcom. For all the polymerswith equal number of carbons in the monomer, the dis-tribution of Ks values with respect to Bsc is plotted inthe Fig. 14. Polymers with side chains that have higherBsc values show higher Ks values. For example, for thepolymers which have eleven carbons in the monomer, weobserve that the polymers with high Ks values also havehigh Bsc values, as represented by the color transitionin Fig. 14. Parameters like Rgsc, Dcom, and Bsc should

be highly useful in polymer informatics, where the keychallenge is the selection of descriptors that can rightlydescribe the polymer structure [39, 40].

FIG. 12. Distribution of the Ks values of 275 polymers.

FIG. 13. Variation of the coil dimensions of polymers withthe Rg of the side chain structure.

IV. CONCLUSIONS

An in silico model to estimate coil dimensions of polyα-olefins in solution has been developed. ExperimentalRg values of PP, P1But, P1Hex and P1Oct were repro-duced, showing that the model is sufficiently accurate.This work provides researchers with a tool capable ofeasily assessing the effect of tacticity and compositionon the coil dimensions of polyolefins. By virtual high-throughput screening, we identified regions in the chem-ical space where the coil dimensions of polyolefins areoptimum. The results from this work provide guidancefor experimentalists prior to extensive synthetic efforts,

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FIG. 14. Variation of the coil dimensions of polymers withthe bulkiness factor of the side chain structure.

and could therefore be a promising tool for acceleratingthe discovery process.

SUPPLEMENTARY MATERIAL

The supplementary material accompanying this pa-per includes the library of 275 polymers and their cor-

responding Ks values. The supplementary informationalso includes the trajectories of iPP, sPP, iP1Dodec, andsP1Dodec simulations.

ACKNOWLEDGMENTS

We acknowledge Patrick Brant (ExxonMobil Chemi-cal Company) for his input on the relationship betweenRg and Mw, and for answering our questions related tothe experimental data. We thank Thomas Sun (Exxon-Mobil Research and Engineering) for providing us withraw experimental data of PP and P1Oct for comparison.We also thank Joseph Moebus (ExxonMobil ChemicalCompany) and Liezhong Gong (ExxonMobil Researchand Engineering) for critical discussions regarding errorpropagation/analysis used in this report. We also ac-knowledge Andy Tsou (ExxonMobil Chemical Company)and Jingwen Zhang (ExxonMobil Chemical Company)for helpful discussions regarding polyolefins and their ap-plications. Finally, we thank Gustavo Carri (ExxonMobilResearch and Engineering) for his input regarding molec-ular dynamics methods. Computing time on the highperformance cluster was provided by Upstream Informa-tion Technology.

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