Systematic study of glass transition in low-molecular phthalonitriles: Insight fromcomputer simulationsD. V. Guseva, A. V. Chertovich, and V. Yu. Rudyak Citation: The Journal of Chemical Physics 145, 144503 (2016); doi: 10.1063/1.4964616 View online: http://dx.doi.org/10.1063/1.4964616 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/145/14?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Rigidity and soft percolation in the glass transition of an atomistic model of ionic liquid, 1-ethyl-3-methylimidazolium nitrate, from molecular dynamics simulations—Existence of infinite overlapping networks in afragile ionic liquid J. Chem. Phys. 142, 164501 (2015); 10.1063/1.4918586 Ultraviolet and visible Brillouin scattering study of viscous relaxation in 3-methylpentane down to the glasstransition J. Chem. Phys. 137, 094504 (2012); 10.1063/1.4748354 The glass transition and the distribution of voids in room-temperature ionic liquids: A molecular dynamicsstudy J. Chem. Phys. 136, 204510 (2012); 10.1063/1.4723855 Molecular dynamics simulations of melting and the glass transition of nitromethane J. Chem. Phys. 124, 154504 (2006); 10.1063/1.2174002 A molecular dynamics simulation of the melting points and glass transition temperatures of myo- and neo-inositol J. Chem. Phys. 121, 9565 (2004); 10.1063/1.1806792

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THE JOURNAL OF CHEMICAL PHYSICS 145, 144503 (2016)

Systematic study of glass transition in low-molecular phthalonitriles: Insightfrom computer simulations

D. V. Guseva, A. V. Chertovich, and V. Yu. Rudyaka)

Department of Physics, Lomonosov Moscow State University, Moscow 119991, Russia

(Received 14 July 2016; accepted 26 September 2016; published online 13 October 2016)

Phthalonitrile compounds with Si bridges were recently suggested for producing thermosettingpolymer composites with reduced Tg and thus expanded processing range. The detailed experimentalinvestigation of this class of phthalonitriles is still difficult due to development time and costslimitations and the need to take into account the structural changes during the crosslinking. In thispaper, we try to overcome these limitations using computer simulations. We performed full-atomisticmolecular dynamics simulations of various phthalonitrile compounds to understand the influenceof molecular structure on the bulk glass temperature Tg. Two molecular properties affect Tg of theresulting bulk compound: the size of the residue and the length of the Si bridge. The larger residueslead to higher Tgs, while compounds with longer Si bridges have lower Tgs. We have also studiedrelaxation mechanisms involved in the classification of the samples. Two different factors influencethe relaxation mechanisms: energetic, which is provided by the rigidity of molecules, and entropic,connected with the available volume of the conformational space of the monomer. Published by AIPPublishing. [http://dx.doi.org/10.1063/1.4964616]

I. INTRODUCTION

Amorphous solids, or glasses, are distinguished fromcrystalline solids by their lack of long-range structuralorder. At the level of two-body structural correlations,there is no qualitative difference upon vitrifying betweenglassformers and supercooled liquids. Nonetheless, thedynamical properties of a glass are so much slower that theyappear to take on the properties of a solid. Although substantialprogress has been made in recent years to understand the roleof intramolecular barriers, local structure, and time and lengthscales in glass-forming liquids, many questions still remainunanswered even for relatively easy model systems.1–5

From the experimentalists’ viewpoint, the main chal-lenges are associated with determination of individualmolecular coordinates. Only very recently it became possibleto resolve individual atoms6,7 and only in the surface layer,the dynamics of which are generally not representative for thebulk material. This fact diminishes the attempt to determinethe role of local structure in the glass transition phenomena forcomplex molecules. Molecular simulation resolves the lackof knowledge of the atomic coordinates. By its very nature,the coordinate of every constituent particle in the system isknown at all times. However, simulations are always limitedby computer power, and in the case of the glass transition thislimitation is severe.

Atomistic molecular dynamics already showed itself asa powerful tool for studying of glass transition temperature,for any compound from simple glycerol-water mixture8 tocross-linked epoxy networks.9 Even about two decades ago,researchers simulated organic glass formers and were able topredict Tg values, which were in agreement with experimental

a)Electronic mail: vurdizm@gmail.com

values with an accuracy of 10 K.10 The typical style in mostpapers is to select one or two types of molecules and todescribe the bulk properties around the glass transition point.At the same time, nowadays the industry starts to believethat computational material science could be a useful toolfor developing new products and for decreasing developmenttime and costs.11

In this study, we performed computational analysisof the broad range of complex organic liquids, namelyphthalonitriles. We focused on phthalonitrile-containing low-molecular compounds, which were recently suggested forproducing modern thermosetting polymer composites,12 andexamined directly by atomistic simulation the correlationbetween monomer structure and macroscopic bulk properties.Industrial grade heat-resistant and mechanically strongmaterials are traditionally produced from thermosetting epoxyresins and other similar compounds, which are capable ofmaintaining high performance characteristics under influenceof various destructive factors. However, most of the currentlyexisting thermosets have limited heat resistance and began todecompose already at 200 ◦C. One of the common waysto obtain heat-resistant and durable polymer material isan irreversible crosslinking of thermosets based on morethermostable monomers (i.e., crosslinking of polyimides,modified phenolic resins, phthalonitriles). Polymer matricesfor use at temperatures above 370 ◦C may be synthesized fromphthalonitrile monomers. The usual phthalonitrile monomerconsists of two phthalonitrile fragments which are linkedby various aromatic rings. New synthetic approaches to thedevelopment of heat-resistant thermosets, including thosebased on phthalonitriles, were investigated experimentallyfor several decades and are currently well represented inliterature.12–15 However, most of the synthesized phthalonitrilemonomers have a high curing temperature and quite narrow

0021-9606/2016/145(14)/144503/7/$30.00 145, 144503-1 Published by AIP Publishing.

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144503-2 Guseva, Chertovich, and Rudyak J. Chem. Phys. 145, 144503 (2016)

and inconvenient processing temperature range. Recentexperiments have shown that modification of phthalonitrilemonomers with siloxane and phosphate bridges drasticallyreduces the resins’ Tg, and thus expands their processingwindow.12,15 However, the experimental investigation of thisclass of phthalonitriles is still difficult due to time andcost limitations, and the need of taking into account thedependence of the reactivity of monomers on their structure,as well as changes in molecular mobility during the reaction.Understanding of the influence of initial monomer structureand the way of crosslinking on the resulting compositesTg may lead to the synthesis of materials with uniquethermo-mechanical properties, with both enhanced stiffnessand toughness and thermal stability at extreme temperatures.

While there are probably hundreds of papers aboutmolecular dynamics estimation of Tg, below we mentionseveral notable studies which are most relevant to our case.In Ref. 16, molecular dynamics comparison of the meltingpoints and glass transition temperatures for two closely relatedsaccharides (namely, myo- and neo-inositol) was performed.These two isomers differ in only one aspect of molecularconfiguration: myo-inositol has only one hydroxyl group inan axial position whereas neo-inositol has two groups. Thispaper demonstrates that even a small change in molecularstructure leads to a substantial increase in a melting point,the observed MD difference was determined to be equal25 K, while it reaches 90 K in lab experiments. In Ref. 17,computer simulations of organic glass former ortho-terphenylin bulk and freestanding films were performed to providemolecular insight into the confinement effect. The torsionalangle distribution of the two side phenyl rings with thecentral phenyl ring was computed and the potential energywas compared with the values found from experimental andtheoretical calculations. It was found that individual ringsreorient faster in comparison with the whole molecule at highertemperatures whereas at lower temperatures the moleculesrelax as a whole. Qualitatively authors conclude that the glasstransition temperature in a freestanding film is reduced.

Jiang et al.18 investigated the influence of the freeorganic groups on the carbon nanotubes (CNT) surface on theglass transition temperature of the epoxy/CNT composites.The Tg was strongly affected by embedded CNTs and freeorganic groups in the CNTs. The Tg of the CNTs/epoxycomposites increased with embedding of CNTs. However,Tgs of the composites decreased with the embedded CNTsfunctionalized by –OH or –COOH groups, and the morevolumetric –COOH groups caused a greater decrease in theTg. The authors explain that by the increase of the interspacebetween the OH–CNTs or COOH–CNTs and the epoxymatrix. Thus, there was more free volume for the epoxychain segments to change their positions, even at a relativelow temperature, inducing a lower Tg.

Recently, Odinokov et al.19 studied a molecular liquidconsisting of dicarbazolylbiphenyl molecules near the glasstransition temperature by molecular dynamics simulations. Inorder to analyze relaxation dynamics, the obtained trajectorieswere re-mapped to represent a model system of oriented point-like particles corresponding to individual molecules. Usingthis approach, authors computed the dynamical susceptibility

and the corresponding relaxation times. Incorporation of orien-tational effects into the density correlation made it possible tocompute the dynamical susceptibility. It should be noted, how-ever, that this model imposes severe restrictions on the typeof the molecules under consideration. In many cases, complexorganic molecules have rather tricky shape and undergo ma-jor conformational changes. In this situation, some intramo-lecular degrees of freedom must be included in the model.

In this paper, we overcome these restrictions byanalysing the relaxation of intermolecular vectors of complexphthalonitrile monomers. In our recent paper,15 we havepredicted Tg for a series of low-melting phthalonitrile bulksamples, including ones which are not synthesized yet.These estimations of Tg were in good agreement withexperimental results in terms of the correct relative Tg

position and similar overestimation values for all samples.In this paper, we perform more systematic study of a setof phthalonitrile monomers. We setup isothermal-isobaric(NPT) molecular dynamics simulation of bulk samples ofphthalonitrile monomers with siloxane bridges, and discuss inmore detail the local structural (glass transition temperature)and dynamical properties (local monomer dynamics) duringglass transition. We examine the influence of the length of thelink between Si atom and the surrounding phenyl rings, as wellas of the volume of residues on Si atom, on the glass transitiontemperature. Thus, the general aim of this study is to find thesystematic route to suitable and easy-processed phthalonitrilemonomers for the future high performance matrices.

II. MODELS AND METHODS

We have analysed bulk properties of nine phthalonitrilemelts of monomers, shown in Fig. 1. These monomers varyby the type and the size of residues in the central part (R1, R2)as well as by the length of the bridge linking central part ofthe molecule with phenyl groups.

A. Molecular dynamics simulations

The fully-atomistic molecular-dynamics simulations werecarried out using GROMACS20,21 package to predict glasstransition temperature Tg of various phthalonitrile bulks. Inthis section, we briefly describe the model and methods usedin our simulations.

Previously,15 we have studied systems of various sizesand at various cooling rates. It was shown that systems of 160monomers are large enough to give consistent results on Tg.We use the same system size in this paper. The initial topologyand conformation of the phthalonitrile monomers werecreated using BIOVIA Materials Studio.22 The correspondingbulks were further prepared implementing the multiscalemethodology of Komarov et al.23 and Gavrilov et al.24 Theresulting bulks at normal atmospheric pressure p = 1 atmand T = 600 K have dimensions from 5.2 × 5.2 × 5.2 nm3 to5.9 × 5.9 × 5.9 nm3, depending on the monomer. Periodicboundary conditions were used in all three directions.The pcff25 force field was used to describe interatomicinteractions. The same methodology and force field wereused in the recent papers for the simulation of polyisoprene-

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FIG. 1. List of monomers: (a) 1a-c,with short linker; (b) 2a-e, with mediumlinker; (c) 3, with long linker.

silica composites26,27 and phthalonitrile bulks.15 Equilibrationand production MD runs were carried out in NPT ensembleat the pressure of p = 1 atm using GROMACS simulationpackage. All the non-bonded atoms in the systems interactthrough a truncated Lennard-Jones (LJ) 9–6 potential witha 1 nm cutoff. The bonded interactions are described withthe angle bending, torsion interactions, and improper dihedralpotentials. The bond lengths are constrained with LINCSalgorithm.21 The charged atoms interact through a Coulombpotential. The temperature and pressure were fixed by usingBerendsen thermostat and Berendsen barostat, respectively.All other simulation parameters and algorithms of calculationwere kept the same as in the recent papers.15,26 The trajectorywas saved every 2 ps. The systems were equilibrated, first, for20 ns at T = 600 K, then for 20 ns at T = 400 K, and finally,for 30 ns at T = 600 K.

For the calculation of glass transition temperature, theequilibrated systems were gradually cooled down fromT = 600 K to T = 100 K at cooling velocity of 5 K/ns, whichallowed to keep statistical error of Tg estimation under ±10 Kfor these systems.15 For the segmental dynamics analysis ateach intermediate temperature, the production MD runs werealso performed for 10 ns.

B. Estimation of glass transition temperature

Glass transition temperatures Tg were estimated fromthe density–temperature plots. To exclude subjective factor inestimations, we used the following algorithm in analysis. Foreach plot, the rough position of glass transition was chosen,effectively dividing all data into two datasets: below and aboveTg. Then each dataset was filtered to maximize R2 of linearapproximation, with the condition of minimum 4 points ineach dataset. The datasets with maximum R2 were used forlinear estimations of ρ(T). Tg point was then defined as theintersection of these two lines. Error S(Tg) was estimatedwhich is based on errors for line parameters obtained in leastsquares method.

C. Estimation of relaxation times

Monomer segmental dynamics were analysed by calcu-lating autocorrelation functions of relaxation of monomer

vectors 2–1, 2–4 and angle 2–3–4 (Fig. 2), characterizingthe monomer internal degrees of freedom. The geometricalpoints 1, 2, 4, and 5 were measured as the centres ofcorresponding phenyl groups, while point 3 as the centreof the Si atom. The following autocorrelation functions werecalculated:

Pu2 (t) =

12

3(u(t0)u(t0 + t))2 − 1

,

for the directions u = {2–1,2–4},

Pγ2 (t) =

12

3 ((γ(t0) − γ̄(T)) · (γ(t0 + t) − γ̄(T)))2 − 1

,

where γ is the angle 2–3–4 and γ̄(T) is an averagevalue of angle 2–3–4 at current temperature T . Pγ

2 (t)has been also normalized. In order to extract correspond-ing orientational relaxation times, these autocorrelationfunctions were fitted with the Kohlraush-Williams-Watts(KWW) function28 P2(t) ≈ exp(−( t

τ)β), where τ is the

characteristic relaxation time, β is the stretching exponentwhich represents the non-exponential character of therelaxation.

FIG. 2. Monomer internal degrees of freedom measurements explained. (a)The chemical structure of the sample of monomer series 2. Geometricalpoints: 1, 2, 4, and 5 are measured as the centers of corresponding phenylgroups, 3 measured as position of Si atom. (b) The atomistic structure ofmonomer 2c. Vectors 2-1 and 2-4 and angle 2-3-4 are shown on the sampleof 2c molecule.

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144503-4 Guseva, Chertovich, and Rudyak J. Chem. Phys. 145, 144503 (2016)

III. RESULTS AND DISCUSSION

A. Glass transition

Our simulations clearly showed the well-defined glasstransition for all considered compounds. The obtainedtemperature-density curves for all simulated systems arepresented in Fig. 3. The resulting Tgs are shown in Table Itogether with the experimental data for 1a, 2b, 2c, and 2dsamples obtained in Refs. 12 and 15. As it is usually observedin MD simulations, there is an overestimation of Tg valueby 20 ± 3 K in our case. This overestimation comes mostlyfrom the small size of the system and fast cooling rate, whichis limited by computing facilities (even in the case of usingsupercomputer). Nevertheless, the correct relative Tg positionand similar overestimation values for all samples indicate thatour calculated Tg values are reasonable and can be used tostudy the mechanisms of glass transition.

It follows from the numbers, that the glass transitiontemperatures in this set of monomers are determined by twofactors. First, the larger the residues on the Si atom, the higherTg. Obviously, larger residues (like phenyl or naphthalene)

FIG. 3. Temperature dependencies of phthalonitrile bulk densities. The ver-tical arrows indicate the calculated Tgs: (a) Series 2 (with medium linker)in ascending order of residue volumes, 2a: 284±8 K, 2b: 292±5 K, 2c:300±5 K, 2d: 319±8 K, and 2e: 368±4 K; (b) Compounds with the sameresidues in ascending order of linker length, 1b: 328±7 K, 2c: 300±5 K, and3: 297±8 K.

TABLE I. Comparison of glass transition temperatures of various phthaloni-trile monomers. L denotes the linker length.

Name L R1 R2 Vres, Å3 Tg, K (sim) Tg, K (exp)

1a 2 Me Me 158 317 ± 6 . . .1b 2 Ph Me 250 328 ± 7 30015

1c 2 Ph Ph 342 342 ± 7 . . .2a 3 H H 0 284 ± 8 . . .2b 3 Me Me 158 292 ± 5 27515

2c 3 Ph Me 250 300 ± 5 28512

2d 3 Ph Ph 342 319 ± 8 30012

2e 3 Nph Nph 486 368 ± 4 . . .3 4 Me Ph 250 297 ± 8 . . .

hinder molecular relaxation due to more dense packing ofthe molecule. Second, the longer the linker connecting theSi atom and the surrounding phenol rings, the lower Tg. Thelonger linker increases the flexibility of the molecule, makingits relaxation easier and faster, which shifts glass transition. Toshow both tendencies at once, we plotted Tg values on the 2Dplot (Fig. 4). Here one axis represents the total residue volume,and second axis is the linker length. Volume of each residuewas defined as intersection of van der Waals radii-spheresand calculated with an accuracy of ±5 Å3. Linker length wasdefined as the number of chemical bonds from the Si atomto phenyl circle, which is two for monomers 1a-c, three formonomers 2a-e, and four for monomer 3. The resulting plotshows steady trends in both axes: small and flexible monomershave the lower Tgs, while compounds with shorter linker andlarger residues have the higher Tgs.

B. Relaxation mechanisms

We started to investigate the relaxation mechanisms inour systems with the analysis of the phthalonitrile bulksin the liquid state at T > Tg. As shown in Refs. 29 and30, glassforming liquids can be divided into “strong” and“fragile” using Angell plot technique. “Strong” liquids likeSiO2 have almost linear (i.e., Arrhenius) behavior, while“fragile” ones (like toluene) display substantial non-linearity.

FIG. 4. Dependence of the simulated Tg on the residue volume and the linkerlength, constructed from the data for nine phthalonitrile monomers.

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144503-5 Guseva, Chertovich, and Rudyak J. Chem. Phys. 145, 144503 (2016)

FIG. 5. Angell plot for the relaxation time of angle 2-3-4. Dashed line showsthe behaviour of ideal strong liquid. Curves for phthalonitrile bulks understudy are significantly lower, which classifies these compounds as “fragile”liquids.

The corresponding plot of the relaxation time τ(234) versusTg/T is shown in Fig. 5. The temperature dependencies lyingdeeply below ideal strong liquid (dashed line in Fig. 5) indicatethat all simulated systems belong to the “fragile” liquids. Thusthe relaxation mechanisms which are responsible for the glasstransition are mostly of intermolecular nature. Moreover,there is almost no difference or some well-defined trends inthese curves. This is why we perform more comprehensive

analysis of the segmental relaxation behavior connected withthe internal degrees of freedom.

For both compounds of series 1 and 2 (short andmedium linker correspondingly), relaxation time graduallyincreases with enlargement of residue volume at all T > Tg.Figs. 6(a) and 6(b) show temperature dependencies of therelaxation time for the angle 2-3-4. Relaxation times of thevectors 2–1 and 2–4 have very similar behaviour and thus arenot shown here. This data are in agreement with observationsof Section III A. However, Figs. 6(c) and 6(d) indicate non-uniform changes in temperature dependencies of relaxationtimes τ of the angle 2-3-4 and the vector 2–1 for compoundswith various linker lengths. The vertical blue arrows on theseplots show the crossings of the curve for compound 3 curvewith data for compounds 1b and 2c. These intersections ofrelaxation time curves refer to different relaxation mechanismsat various temperatures above Tg for these monomers (or atleast for some of them).

Compound 1b with the shortest linker has the smallestrelaxation time at 600 K, but with reduction of temperatureit increases more rapidly in comparison with compounds2c and 3. Presumably, it can be explained by two differentfactors influencing the relaxation mechanisms: energetic (i)and entropic (ii). The first is provided by the rigidity of themolecules, the increase of which leads to slower relaxationrates and higher Tg. The growth of relaxation time withincrease of volume of the residues indicates the presence ofthis factor. Clearly, the linker length also can be consideredas a rigidity factor, as the longer linkers with CH2 groups

FIG. 6. Temperature dependencies of relaxation time for (a) angle 2-3-4 in monomers 1a-c; (b) angle 2-3-4 in monomers 2a-e; (c) angle 2-3-4 in monomers 1b,2c, and 3; (d) vector 2-1 in monomers 1b, 2c, and 3. Colored vertical dashed lines show glass transition temperatures of corresponding monomers. Blue arrowsindicate curves intersection points.

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144503-6 Guseva, Chertovich, and Rudyak J. Chem. Phys. 145, 144503 (2016)

FIG. 7. Probability distribution of the angle 2-3-4 averaged over temperaturerange of 520–600 K for monomers 1b, 2c, and 3.

allow more freedom to the intermolecular transformations.At temperatures slightly above Tg, it makes perfect sense:bulks of monomers with longer linker have lower relaxationtimes at T in the range of 300–350 K. However, at highertemperatures, short linker molecules show steeper reductionin relaxation time with increasing temperature. This tendencyis not observed for the molecules with the same linker andvarious residues. Thus, there is a second factor with an effectopposite to the effect of the first one.

We suppose that the second factor has the entropicnature and is connected to the available volume ofmolecular conformational space. At low temperatures, theconformational space is confined and the relaxation time,which is determined by the time needed to observe theconformational space, is small. Simultaneously, at highertemperatures, the relaxation times increase because of morecomplex conformational space these monomers belong to.Some estimation of the available conformation space could bedone while analyzing the probability distribution of the angle2-3-4 presented in Fig. 7: the smaller the linker length themore narrow bell-curve we have. This is a typical behaviorfor polymer-like molecules, where the chain entropy andcorresponding free energy depends strongly on the chainlength N .31 However, at lower temperatures slower motion inconformational space is compensated by its shrinking, keepingrelaxation time curves for systems 2c and 3 more flat than forsystem 1b.

IV. CONCLUSIONS

In this paper, glass transition Tg of phthalonitrile bulkswas studied by molecular dynamics simulations. It was shownthat two molecular properties affected Tg in the bulk state.The first is the size of residues. The larger residues lead tohigher Tg due to denser packing of the molecule. The secondfactor is Si bridge length. Longer bridges are more flexible,which increases overall flexibility of the molecule and lowersTg. Detailed analysis of intra-molecular relaxation indicatedthe presence of two relaxation mechanisms, called energy-and entropy-driven relaxation. The energy-driven relaxation

mechanism is provided by the rigidity of the molecule. Theentropy-driven relaxation mechanism is connected to theavailable volume of the conformational space of the monomer.The correlation between these mechanisms and molecularproperties of the monomers makes it possible to design themonomer with the desired relaxation properties as well as Tg.

SUPPLEMENTARY MATERIAL

See the supplementary material for details on KWWfitting of autocorrelation functions and estimation of errors inrelaxation times.

ACKNOWLEDGMENTS

This work is supported by Russian Foundation for BasicResearch, Research Project Nos. 15-31-70007\15 and 16-33-60215\15.

The simulations have been performed using the facilitiesof the Lomonosov Moscow State University ResearchComputational Center.32

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32See http://hpc.msu.ru for information about the Lomonosov Moscow StateUniversity Research Computational Center.

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