5002 | Soft Matter, 2016, 12, 5002--5010 This journal is©The Royal Society of Chemistry 2016

Cite this: SoftMatter, 2016,

12, 5002

Raman analysis of bond conformations in therotator state and premelting of normal alkanes†

Anthony P. Kotula,a Angela R. Hight Walkerb and Kalman B. Migler*a

We perform Raman spectroscopic measurements on normal alkanes (CnH2n+2) to quantify the n

dependence of the conformational disorder that occurs below the melt temperature. We employ a

three-state spectral analysis method originally developed for semi-crystalline polyethylene that posits

crystalline, amorphous, and non-crystalline consecutive trans (NCCT) conformations to extract their

respective mass fractions. For the alkanes studied that melt via a rotator phase (21 r n r 37), we find

that conformational disorder can be quantified by the loss of NCCT mass fraction, which systematically

decreases with increasing chain length. For those that melt directly via the crystal phase (n Z 40), we

observe NCCT conformational mass fractions that are independent of chain length but whose

disordered mass fraction increases with length. These complement prior IR measurements which

measure disorder via gauche conformations, but have not been able to measure the mass fraction of

this disorder as a function of n. An interesting feature of the three-state analysis when applied to alkanes

is that the measured fraction of disordered chain conformations in the rotator phase of (10 to 30)%

greatly exceeds the mass fraction of gauche bonds (1 to 7)% as measured from IR; we reconcile this

difference through DFT calculations.

Introduction

Normal alkanes CnH2n+2 comprise a variety of materials rangingfrom paraffin wax to polyethylenes. In addition, alkane chainsegments are an important constituent of biological moleculesincluding fatty acids, long-chain alcohols, and phospholipids.Chain configuration and packing of these molecules directlyimpacts the physical properties that are critical to industrialprocessing. Therefore, identifying and quantifying the differentstructural changes in alkanes is a crucial step towards theefficient handling of these systems at the industrial scale.1,2

Despite having a simple repeat unit, normal alkanes exhibita wide variety of structural changes with temperature. Alkaneslonger than C9H20 (abbreviated as C9) with an odd number ofcarbon atoms have an orthorhombic packing as the lowestenergy structure. This crystal phase consists of alkane moleculesin the trans configuration forming stacked lamellae with thelong axes of molecules parallel. A cross section of the lamellaecut perpendicular to the chain axis would reveal molecularorientation resembling a herringbone pattern.

The transition between the orthorhombic crystal to the hightemperature melt phase is known to depend strongly on n and

is mediated by disorder. For 9 r n r 39 alkanes undergo atransition to a rotator phase a few degrees below the meltingpoint.3–6 Within this phase the molecules lose their herring-bone order, but remain in the trans configuration in lamellarstacks, which we refer to as non-crystalline consecutive trans(NCCT). Disorder in the rotator phase takes the form of singlegauche (G) and gauche–trans–gauche ‘‘kink’’ (GTG0) conformationsas well as twist solitons.7 For n 4 39 there is no stable rotatorphase; instead the formation of nonplanar conformers occurs justbelow the melting point.8 Premelting is a thermodynamically-favored surface melting of the alkane crystal characterized by theappearance of gauche bonds and possibly chain segments that areNCCT near the chain ends. In the crystal phase, a decrease from100% crystalline fraction and appearance of NCCT conformers is asignature of conformational disorder; likewise, in the rotatorphase, a decrease from 100% NCCT fraction and appearance ofamorphous conformers is a signature of conformational disorder.

In the present work, we are concerned with the nature and ndependence of disorder that occur in the rotator phase andduring premelting. A thorough understanding of these statesprovides important information on the nature of the meltingtransition and underlying thermodynamics. Vibrational spectro-scopy is the primary tool to measure conformational states inthe crystal and rotator phases of alkanes but there are criticalgaps in our ability to measure the n dependence of disorder.9,10

Infrared (IR) spectra have been used to identify and quantifyspecific gauche–trans sequences along the chain in both the

a Materials Science & Engineering Division, NIST, Gaithersburg, Maryland 20899,

USA. E-mail: kalman.migler@nist.govb Physical Measurements Laboratory, NIST, Gaithersburg, Maryland 20899, USA

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c6sm00182c

Received 22nd January 2016,Accepted 9th May 2016

DOI: 10.1039/c6sm00182c

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crystal and rotator phases.5,11,12 Phase transitions betweendifferent crystal structures, as well as the crystal–rotator androtator–melt transitions, have been correlated with changes inthe intensities of CH2 rocking modes in the IR spectra ofalkanes.13 The IR spectra of selectively deuterium-labeledalkanes have been used to show that gauche bonds tend toappear at the ends of the alkane chain in the rotator phase andbecome more probable with increasing temperature.14 While ithas been shown that the number of gauche bonds per chainincreases with chain length in the rotator phase, the experimentaluncertainty prevents a conclusion as to whether there is anincrease in the fraction of gauche bonds. The ability to measurethis would yield critical information regarding the disappearance ofthe rotator phase for n 4 39. Likewise, measurement of disorderedchain conformers during premelting could directly quantify the‘‘melted’’ chain segments theorized by Flory and Vrij15 whichcan only be inferred from specific gauche bonds using IR.8

Raman spectroscopy in the fingerprint region providescomplementary information to IR and may be able to fillgaps regarding disorder in the rotator phase and premeltingphenomenon. The transition from an orthorhombic crystalphase to a rotator phase has been shown to correlate with theloss of a CH2 bend peak near 1416 cm�1.16,17 Ab initio calculationshave shown that intensity changes in the C–C stretch and CH2

twist regions can be correlated with the number of consecutivetrans bonds along a single alkane chain.18,19 In polyethylene,Raman spectroscopy in the CH2 twist and bend regions have beenused to provide quantitative information on the mass fraction ofthree conformational states: amorphous gauche-rich conformers,orthorhombic crystalline conformers, and non-crystalline con-secutive trans (NCCT) sequences.20,21 Through measurement ofthese three states in the alkanes as a function of n, we hope toshed light on the melting transitions.

While the three-state measurement analysis is well documentedin polyethylenes there are questions on how to apply it toalkanes. An important question is the relationship betweenthe mass fraction of (NCCT and amorphous) chain conformersmeasured via Raman with the total mass fractions of gauche andtrans conformers present on the alkane chain. Our initial Ramanspectroscopic measurements of a C21 alkane in the rotator phaseindicate (10 to 30)% amorphous conformers.21 This disorderedfraction significantly exceeds the mass fraction of gauche bondsestimated from IR measurements of the C21 alkane, which areon the order of (1 to 7)%.14,22 These differences must beaddressed to relate Raman measurements to trans and gaucheconformers directly.

In this work, we quantify the chain conformers in the variousphases obtained during heating over a range of n. Alkanes fromC21 to C60 are used to measure amorphous, crystalline, and NCCTchain conformers. We first consider the Raman spectra of C23 andC41 as representative examples of alkanes that exhibit either arotator phase or premelting, respectively. We show that themass fraction of NCCT conformers decreases with chain length,and further varies depending on whether the alkane exhibits arotator phase. A simple conversion allows us to calculate themaximum number of NCCT bonds per chain generated during

the melting process. These measurements are supported bydensity functional theory (DFT) calculations of Raman spectrawhich relate the disordered mass fraction to the type of gauchesequence and also provide information on the effect of gaucheconformations as a function of position along the chain.

These measurements are important because an increase inthe number of gauche bonds is expected to reduce the lamellarspacing in the rotator phase of alkanes,23 and the fraction ofgauche conformers per chain has been implicated as a drivingforce for rotator–rotator and rotator–melt transitions.23–25 Boththe temperature and type of rotator–rotator phase transition isexpected to depend on gauche bonds.25 The gauche concentrationincreases through the crystal–crystal transitions,13,24,26 and chaintilt within alkane layers has been attributed to more efficientchain packing due to increased gauche bonds near chainends.25,27 Molecular dynamics simulations of alkane chains28,29

which directly calculate gauche and trans bond distributions andmean field calculations of alkane packing disorder30 couldbenefit from an experimental determination of gauche and transconformer mass fractions. Raman spectroscopic measurementson a wide range of alkanes would provide both quantitativeinformation on the distribution of conformers in differentphases as well as provide guidance for potential structures ofNCCT precursors in crystallizing polyethylenes.

Materials and methods

Table 1 shows the alkanes used in this work (see Disclaimer).The minimum purity of the alkanes were in the range of (95 to99.5)%, with the C37 alkane having a purity of 95% and theremaining alkanes all having a minimum purity of at least 98%.Large alkane flakes present in the purchased alkanes arebroken into smaller pieces prior to sample loading to generatea homogeneous scattering volume for measurement.

Alkanes are loaded into a Linkam shear cell (CSS 450,Linkam Scientific Instruments Ltd) by filling a 3/8 inch innerdiameter Nitrile standard O-ring placed on the bottom quartzplate, then compressing the sample to a gap thickness of 1 mm.The shear cell is not used in a shearing mode for theseexperiments, but it provides optical access to the sample at acontrolled temperature. Raman measurements are performedin a 1801 backscattering mode using a triple grating spectro-meter (Horiba T64000) with a spectral resolution of 0.8 cm�1.The sample is excited using linearly polarized light from a

Table 1 Normal alkanes used in this work

Name Molecular formula Brand Nc

Heneicosane C21H44 Fluka 0.48 � 0.02Tricosane C23H48 Aldrich 0.46 � 0.03Pentacosane C25H52 Aldrich 0.45 � 0.03Heptacosane C27H56 Sigma-Aldrich 0.58 � 0.03Heptatriacontane C37H76 Aldrich 0.58 � 0.03Tetracontane C40H82 Fluka 0.54 � 0.03Hentetracontane C41H84 Fluka 0.47 � 0.03Pentacontane C50H102 Aldrich 0.46 � 0.03Hexacontane C60H122 Aldrich 0.50 � 0.04

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632.8 nm HeNe laser focused to a spot size of approximately60 mm. The laser is kept at a power level of 30 mW. The longeralkanes (C50 and C60) exhibit strong background fluorescencethat is bleached from the sample over a period of 30 minutesusing the laser at the maximum intensity. The spectra for thesealkanes is collected using a 30 s acquisition time. Spectra of thealkanes in the range of C21 to C41 exhibit minimal backgroundfluorescence and are collected using a 15 s acquisition time.Two accumulations of spectra are averaged together within theLabSpec software (LabSpec 5, Horiba) to improve spectrumquality and remove cosmic rays using a spike filter.

The assignment of fundamental vibrations to various Ramanbands have been well-documented in the literature.9 Ramanspectra are analyzed using a nonlinear least-squares algorithmto determine the best-fit Lorentzian peaks to the experimentalprofile. An initial guess for the peak widths are estimated fromfits of the spectra at room temperature and a temperature atleast 10 1C greater than the melt transition. A linear baselinewas simultaneously fit to the spectra. A maximum of 4 peaks inthe range of (1430 to 1500) cm�1 are included to improve the fitof the crystalline CH2 bend peak but are not used in theanalysis. The 95% confidence interval on the curve fit is usedto calculate the standard error in the peak height, width, andposition. The error bars shown in Fig. 2 through 4 are theestimated standard error in the calculated value based on thestandard error in the peak height and width using propagationof error techniques.

The alkanes are heated in a stepwise fashion from roomtemperature in increments ranging from (0.5 to 10) 1C at a rateof 30 1C min�1, then held at the measurement temperature forapproximately 2 min before collecting spectra. The temperatureof the Linkam shear cell is calibrated using the melting pointstandards benzoic acid and 4-methoxybenzoic acid purchasedfrom Sigma-Aldrich. Melting of these standards is determinedoptically, and the reported temperatures are accurate to within�0.5 1C. Multiple output spectra are generated over a time periodof approximately 5 min; post processing is used to determine ifthere are any changes in integrated peak intensities in the (1000to 1500) cm�1 range at a constant temperature. The spectrapresented and analyzed at a given temperature have constantpeak intensities to within measurement error.

The Raman spectra can be used to calculate mass fractionsof conformers using a method described in our previous work21

based on a prior analysis of polyethylene spectra by Strobl andHagedorn.20 The analysis assumes that the chain segments willhave one of three conformations: an orthorhombic crystallineconformation (cr), and amorphous gauche-rich conformation(am), or a trans-rich conformation that is not in an orthorhombiccrystalline configuration, denoted as non-crystalline consecutivetrans (NCCT). A mass balance dictates that the mass fractions ofthese components must sum to 1:

aam + acr + ancct = 1. (1)

The individual mass fractions are calculated based on the followingprocedure: first, Lorentzian profiles are fit to the Raman spectrain the (1000 to 1500) cm�1 region. Next, the integrated intensities

I of each peak are normalized by an invariant Itw, which is thesum of the trans- and gauche-rich CH2 twist peak intensities:

Itw = I (1296 cm�1) + I (1304 cm�1). (2)

Normalized peak intensities are denoted by I0. The disordered massfraction in an amorphous conformation is directly calculated fromthe normalized CH2 twist peak intensity of gauche-rich conformersaam = I0(1304 cm�1). The mass fraction of material that is not in theamorphous conformation is act = I0(1296 cm�1), the mass fraction ofconsecutive trans conformers. Based on ab initio calculations,19

alkane chains with sequences of fewer than 5 trans bonds will notgenerate a sharp peak in the CH2 twist (trans) position and insteadcontribute to the broad amorphous peak located experimentally at1304 cm�1. This means that the disordered mass fraction cancontain smaller sequences of trans bonds distributed among gauchebonds. The consecutive trans mass fraction is equal to the sum ofchains in the crystalline and NCCT conformations: act = acr + ancct.The mass fraction of crystalline chains is obtained from theintensity of the CH2 bend peak acr = I0(1416 cm�1)/Nc, whereNc is a scale factor. The mass fraction of chains in the NCCTconformation is then calculated via eqn (1).

The scale factor Nc is chosen for each alkane such that, atroom temperature, the alkanes are 100% crystalline. Values ofthe scale factor for each alkane are shown in Table 1. Theuncertainty in Nc is based on propagation of the standard errorin the curve fit to the spectra. For all alkanes, the scale factor isin the range 0.45 o Nc o 0.58. There is no systematic change inthe scale factor with increasing chain length over the range ofalkanes measured, but the scale factors for the C27 and C37

alkanes are greater than one standard deviation away from themean. The range of scale factors are attributed to orientation inthe alkane samples and the strong polarization dependence ofthe CH2 twist and bend modes for the alkanes.31 This scalefactor is assumed to be constant with temperature.

Results

We start by presenting data for two representative alkanesduring heating. Raman spectra of the C23 alkane at threetemperatures is shown in Fig. 1a. At 25 1C the spectra containsharp peaks in the (1000 to 1500) cm�1 region that are attributedto alkane chains in an all trans conformation along the chainlength and an orthorhombic crystalline packing.9 When thetemperature is increased to 41 1C the crystalline peak at1416 cm�1 is no longer observed, but the strong C–C stretchpeaks at 1060 cm�1 and 1129 cm�1 as well as the sharp CH2

twist peak at 1296 cm�1 are still present. This indicates that thealkane has transitioned from an orthorhombic crystal packinginto a more disordered rotator structure.17 This loss of order isattributed to increasing rotational disorder in the RV phase, inwhich chain segments randomly rotate about the chain axis by�901.32 Increasing the temperature of the alkane above the melttemperature (47.7 1C)4 results in the loss of sharp peaks due totrans conformers in favor of broad spectral features in Fig. 1aattributed to chain segments comprised of both trans and

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gauche conformers.33 Three spectra for the C41 alkane are shownin Fig. 1b. The Raman spectra in the orthorhombic crystal phaseat 25 1C resemble the C23 spectra at the same temperature. Thespectra retains sharp spectral features at temperatures justbelow the melt transition at 84.3 1C,34 including the orthorhombiccrystalline peak. From a qualitative standpoint, there is nocharacteristic change in spectral features that would indicate atransition prior to melting. Increasing the temperature abovethe melt transition generates Raman spectra characteristic ofthe melt state, and at no point during the melting process isthere a rotator phase spectrum similar to the one shown for theC23 alkane.

Fig. 2 shows the mass fraction analysis as a function oftemperature T for the C23 and C41 alkanes. In Fig. 2, we defineancct* (horizontal dashed lines) as the maximum value of ancct

that occurs for a given n over the full temperature range fromcrystal to melt. For the C23 alkane (Fig. 2a), at temperatures lessthan 41 1C, the mass fractions of the amorphous, crystalline, andNCCT conformers remain constant with increasing temperature.The alkane is completely crystalline in this temperature range,with negligible mass fractions of disordered and NCCT material.When the temperature is increased to 41 1C, the sample entersthe rotator state and the mass fraction of chains in the NCCT

conformation increases to its maximum, ancct* (n = 23) = 0.89,while the crystalline mass fraction is reduced nearly to zero.This is determined from the disappearance of the crystallinepeak at 1416 cm�1 in the Raman spectra at 41 1C, as shown inFig. 1a. Increasing the temperature to 42 1C leads to a loss of thecrystalline peak to within measurement sensitivity. The massfraction in the NCCT conformation decreases monotonicallywith increasing temperature in the range of (42 r T r 47) 1C,while the disordered mass fraction increases. When the temperatureexceeds 47 1C an abrupt transition again occurs in the massfraction distribution corresponding to the abrupt loss of thesharp CH2 twist peak at 1296 cm�1, with the disordered massfraction dominating the composition. At this temperature theNCCT mass fraction is approximately 0.03 which is still abovethe measurement threshold. This low mass fraction is in agreementwith rotational isomeric state models for consecutive transsequences in the melt: a trans–gauche energy of approximately2 kJ mol�1 yields trans probabilities near 50% at 50 1C. Theprobability of 5 consecutive trans sequences is then 0.07, nearthe measured NCCT mass fraction in the melt state. Thedisordered mass fraction increases slightly as the temperatureincreases to 60 1C with a simultaneous decrease in the NCCTmass fraction. The corresponding crystal–rotator and rotator–melttransitions based on DSC measurements13 of the C23 alkane agreewell with the sharp mass fraction transitions that occur duringheating. We emphasize that each thermodynamic phase isidentified by a characteristic distribution of chain conformers:the low-temperature crystal phase contains only orthorhombiccrystalline conformers, the rotator phase is comprised mostly ofNCCT conformers with no crystallinity, and the melt phase iscomprised of a majority amorphous chain conformers.

The mass fraction analysis of the C41 alkane versus temperatureshown in Fig. 2b indicate a dramatically different melting profilecompared to the C23 alkane. At this n, no crystal–rotator phasetransition is measured in DSC experiments34 or reported inwide-angle X-ray scattering.35 We observe that the C41 alkane isprimarily crystalline from room temperature to the meltingpoint, above which the alkane is primarily in the melt state –the chain conformer distribution allows a clear identificationof the thermodynamic phases. At temperatures exceeding 70 1Cthe crystalline mass fraction decreases with a correspondingincrease in NCCT mass fraction. The maximum NCCT massfraction, ancct*, occurs at 83 1C, just prior to melting. The C23

and C41 alkanes are representative of the two characteristicclasses of alkanes, and they show dramatically different valuesof ancct*. (The mass fraction of NCCT for all alkanes studied inthis work as a function of temperature are provided in the ESI.†)

The chain length dependence of ancct* for both classes ofalkane are shown in Fig. 3, along with acr* and aam*, which for agiven n are the values of acr and aam that are measured at thecorresponding ancct*. For alkanes exhibiting a rotator phase, ancct*decreases with chain length. Although modest, the systematicdecrease in ancct* indicates that longer alkanes undergoingthe crystal–rotator phase transition at higher temperaturesshow increasing disorder. In contrast, alkanes that only exhibitpremelting have no significant chain length dependence on

Fig. 2 Mass fraction of crystalline, NCCT, and amorphous material in (a)the C23 alkane and (b) the C41 alkane versus temperature. The dashed linesindicate transitions between phases reported by Maroncelli et al.13 andPaunovic and Mehrota.34 The dotted horizontal lines indicate ancct* foreach alkane, defined as the maximum value of ancct that occurs for a givenn over the temperature range.

Fig. 1 Raman spectra of (a) the C23 alkane and (b) the C41 alkane at threedifferent temperatures. The spectra are scaled by the integrated intensityof the CH2 twist region. The dashed line indicates the crystalline peak.

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ancct*. Within both classes of alkane, aam* increases as afunction of n.

The mass fraction information shown in Fig. 3 can be usedto estimate the maximum average number of NCCT bonds perchain to develop a more physical picture of the number ofbonds in a consecutive trans conformation without crystallineorder. For a chain of length n there are n � 3 dihedral angles ofC–C bonds. Since each alkane has a monodisperse chainlength, the maximum average number of NCCT bonds perchain nncct* is estimated by

nncct* = ancct*(n � 3). (3)

Eqn (3) is used to convert the maximum NCCT mass fractionproduced during melting shown in Fig. 3 to the maximumaverage number of NCCT bonds per chain. This value is plottedversus chain length in Fig. 4.

Although ancct* decreases with increasing chain length, thenumber of NCCT bonds per chain increases for chains exhibiting arotator phase. The dependence of nncct* on chain length is linear inthis region as indicated by the dotted line in Fig. 4, with a slope of0.51 � 0.07 and intercept of 6.0 � 1.7. When ancct* occurs duringpremelting, the number of NCCT bonds per chain is independentof chain length within experimental uncertainty.

Note that our Raman based measurements of conformermass fractions do not show abrupt changes at the crystal–crystal or rotator–rotator transitions that have been observed bycalorimetry27,36 and X-ray.23 The smoothly varying NCCT massfraction for C23 (Fig. 2) is qualitatively consistent with thecontinuous change in the lattice distortion reported fromX-ray scattering through rotator–rotator transitions up to45 1C;23 however, the constant hexagonal lattice between 45 1Cand the melting temperature contrasts with the continueddecrease in ancct. This indicates that these crystal–crystal androtator–rotator transitions (and the lattice distortion) are not

associated with sharp changes in the distribution of chainconformers; IR measurements show smoothly varying changesin peak intensities,13 but are not particularly sensitive to thesetransitions. The largest latent heat associated with rotator–rotator transitions is nearly two orders of magnitude smallerthan the enthalpy of melting for alkanes,27 which indicates smallchanges in the chain conformation during these transitions.

In comparing our results to prior vibrational spectra measure-ments, we find that the numerical value of the disordered massfraction aam calculated using our Raman spectroscopic analysisgreatly exceeds the concentration of gauche conformers calculatedfor normal alkanes using IR techniques.8,13,14 Both single gauchebonds that occur near chain ends and gauche–trans–gauche (GTG0)sequences are of interest due to the formation of nonplanar alkaneconformers, as shown in the examples in Fig. 5. The sum of gauchebonds and GTG0 sequences for alkanes in the rotator phase are inthe range of (1 to 7)% via IR measurements,13 which contrasts withthe (10 to 30)% of amorphous conformers that are present inalkanes in the range 21 r n r 37 shown in Fig. 3b. The IRmeasurements of premelting for C50 and C60 alkanes indicateapproximately 0.4 and 0.6 GTG0 sequences per chain respectively,8

which is equivalent to gauche mass fractions on the order of 1%.This is roughly an order of magnitude smaller than the massfraction of amorphous conformers of the C50 and C60 alkanespresent during melting in Fig. 3b.

In resolving this difference between gauche mass fractionsand disordered mass fractions, an analysis of the specific vibrationalmodes used to calculate these conformers is necessary. The IRanalysis of gauche conformers relies on the intensity of CH2 wagpeaks in the (1300 to 1350) cm�1 range to calculate the fractionof chains containing a specific non-trans sequence, with gauchebonds at chain ends evaluated from the 1341 cm�1 peak anda GTG0 sequences indicated by the 1306 cm�1 peak.13 Thewagging modes of alkanes have been analyzed using a simplecoupled oscillator theory to show that these modes are not affectedby methyl end groups.37 The measurement of amorphous and

Fig. 3 Maximum mass fraction of NCCT conformers, ancct*, versus chain

length n. The corresponding mass fractions of crystalline acr* and amor-phous material aam* at the maximum ancct* are also shown. The verticaldashed line separates the lower n alkanes that exhibit a rotator phase fromthe higher ones that do not.6

Fig. 4 The maximum average number of NCCT bonds nncct* versus chainlength n. The dotted line is a linear regression of the nncct* values from C21

to C37. The vertical dashed line indicates the longest alkane chain that stillexhibits a rotator phase.6 The number of NCCT bonds for an all transalkane is indicated by the dash-dotted line.

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NCCT conformers via Raman spectroscopy is based on CH2 twistpeaks in the (1290 to 1310) cm�1 region of the spectrum. Peaks inthis region do not appear to follow simple coupled oscillatortheory,37,38 but the Raman scattering intensities of alkanechains with different amounts of gauche bonds have beencalculated by Meier et al.18,39 using ab initio methods. Thesecalculations indicate that approximately five consecutive transbonds are necessary for the appearance of the sharp 1296 cm�1

peak in the vibrational spectra, whereas consecutive transsequences of two or fewer contribute to the broad CH2 twistpeak located at 1303 cm�1. A sequence of four trans bondsfollowed by a gauche bond would only slightly contribute tothe NCCT peak based on ab initio calculations,19 therefore our(10 to 30)% amorphous conformers measured from Ramanspectra would indicate as few as (2 to 6)% gauche bonds, similarto values reported via IR. We verify this in more detail throughsingle-chain DFT modeling.

For DFT calculations we generate typical chain configurationsfor a C21 alkane with either single gauche bonds or GTG0 sequences(see Fig. 5) and compute the chain normal modes in the CH2

twist region. The normal modes are phenomenologically broadenedto generate peaks that are then analyzed as Raman spectra tocalculate a disordered mass fraction; calculation details andspectra (Fig. 7) are included in the Appendix. These fractions areshown in Fig. 6 for either a single gauche bond or GTG0 sequenceat various positions along the chain. For a single gauche bond,the disordered mass fraction increases with position from thechain end until the seventh bond position and a maximumdisordered mass fraction. Similar behavior is observed for theGTG0 sequence. The dashed and dotted lines indicate the massfraction of gauche bonds input into the DFT calculation for a C21

with either a single gauche bond (one gauche per 18 totaldihedral angles) or a GTG0 sequence (two gauche per 18 dihedralangles), respectively.

Fig. 6 indicates that the numerical value of aam that wouldresult from a Raman measurement must exceed the numericalvalue of the mass fraction of gauche bonds that would resultfrom IR measurement. Over the range of positions, the ratio ofac

am to the gauche mass fraction ranges from 2.4 to 8.5 for a

single gauche bond and 1.4 to 2.9 for the GTG0 sequence.Although single gauche bonds will increase the calculateddisordered mass fraction near the middle of the chain, theoccurrence of single gauche bonds become less probable. PriorIR measurements of the C21 alkane indicate that the largestconcentration of gauche bonds occurs at chain ends in therotator phase and decreases exponentially with bond position.14

We can now compare the ratio between the disordered massfraction via Raman and the gauche mass fraction via IR. Sincethe concentration of gauche bonds is expected to decrease anorder of magnitude by the fifth bond position,14 we assume thatsingle gauche bonds only appear in appreciable concentrationbetween the chain end and the fourth bond position. Based onthis assumption, the disordered mass fraction via Raman shouldbe in the range of 2.4 to 5.4 times the mass fraction of singlegauche bonds for alkanes in the rotator phase. Our measurementsof aam* which range from (10 to 30)% would indicate gaucheconcentrations in the range of (1.9 to 12.5)%. This is similar to the(2 to 7)% reported from IR measurements of alkanes of similarchain length.

In addition, we can use our methodology in combinationwith prior IR measurements to comment on the existence ofsingle gauche bonds for the cases of the C50 and C60 alkanes,where IR was found to be insensitive.8 The scaling factor in therange of 1.4 to 2.9 for GTG0 bonds does not account for theorder of magnitude difference between the Raman disorderedmass fraction measurement for the C50 and C60 alkanes and thegauche mass fraction based on IR measurements of GTG0

bonds. Since the disordered mass fraction is sensitive to bothsingle gauche bonds and GTG0 sequences, we expect that singlegauche bonds are also present in significant quantities duringthe melting of these alkanes. The existence of single gauchebonds near the melting temperature agrees with the qualitativeRaman measurements of Kim et al. performed on the C50

alkane.8 IR measurements indicate that the C60 alkane generatesa mass fraction of approximately 0.02 gauche bonds due solely toGTG0 sequences prior to melting.8 Combining this information

Fig. 6 Calculated mass fractions of amorphous conformers acam of C21

chains with disorder plotted versus bond position. Both single gauchebonds (G) and GTG0 sequences are shown. The intensity ratio is placed atthe trans bond position for alkanes with a GTG0 sequence.

Fig. 5 Structures of a C21 alkane in an all trans conformation and witheither a single gauche bond or GTG0 sequence.

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with the maximum disordered mass fraction of 0.08 measuredvia Raman spectroscopy indicates that single gauche bonds arepresent in a mass fractions of less than 0.02, which indicates thatgauche bonds and GTG0 sequences are present in concentrations ofcomparable magnitude when the C60 alkane exhibits premelting.

Discussion

Although we have assumed that dihedral angles can only existin a trans or gauche conformation, localized 1801 twists (called‘‘twist solitons’’) could also be present along the alkane back-bone owing to small systematic perturbations in consecutivedihedral angles.40 These structures have been proposed tointerpret NMR measurements of motion in polyethylene lamellae,41

and more recent investigations of the C23 alkane have sought tocharacterize twist solitons in the crystal and rotator phases bothcomputationally and analytically.7 IR peak intensities appearsensitive to solitons in the C–C stretch region for a C19 alkane inthe rotator phase near the melting temperature.42 We cannotrule out the presence of twist solitons or effect of these structureson Raman intensities. However, we note that the mass fractionanalysis does not include Raman-active C–C stretch modes.Since the total integrated intensity of the CH2 twist region isconstant, we expect that spectral features due to twist solitonswill be overshadowed by either the sharp trans peak or broadamorphous region.

Prior molecular dynamics simulations of finite chains showqualitative similarities to our results. Simulations of C19 alkane43

and C23 alkane44 systems show increasing gauche bonds at thechain ends during the crystal–rotator phase transition, whichagrees with the increase in the mass fraction of amorphousconformers observed in our experiments.

Our mass fraction measurements over the range of alkanechain lengths provide insight into the effect of chain motion ondisorder for the longer alkanes. As chain length increases,alkanes preferentially exhibit segmental motion along the chainaxis, which causes premelting of chain ends in lieu of a rotatorphase.45 The sharp decrease in the disordered mass fractionwhen increasing chain length between the C37 and C40 alkanesin Fig. 3b indicates that the shortest alkanes that do not exhibita rotator phase also have the least segmental motion of thepremelting alkanes. Chains longer than the C40 alkane have ahigher melting temperature and therefore more thermal energyfor segmental motion prior to melting. The effect of thisincreased motion is a larger fraction of conformationally dis-ordered chain segments, which is evident in our measurementsof the disordered mass fraction with increasing chain length.

A significant benefit of the mass fraction analysis comesfrom the direct relationship between the chain conformerdistribution and the thermodynamic phase of the alkane.Similarly, sharp transitions in the mass fraction distribution occurat phase transition temperatures as shown for the C23 and C41

alkanes. Sharp transitions in peak intensities are also reported in IRspectra at transitions between the crystal, rotator, and melt phases;13

however, the IR analysis does not yield quantitative information onthe conformer distribution in each phase.

Both the mass fraction of gauche conformers and the massfraction of amorphous conformers are crucial aspects of theoreticalmodels of phase transitions in linear alkanes. Theoretical modelsof partial melting in alkanes15 depend on some amount ofterminal methyl groups being ‘‘melted.’’ This ‘‘melted’’ amountis not calculated directly, but must be inferred through thermalmeasurements. Prior measurements note that the amount of‘‘melted’’ methyl groups is significantly greater than the amountof gauche bonds per chain by a factor of 3.0 to 4.5 due to thedisruption of the crystalline lattice by the gauche bond,8 which iswell within the range of ratios between disordered and gauchemass fractions estimated via our calculations. Therefore, themass fraction analysis of Raman spectra provides a direct estimationof the ‘‘melted’’ methyl groups through the disordered massfraction. This result further highlights the complementarynature of IR and Raman spectroscopy: while IR measurementsare sensitive to the type and concentration of specific gauchebond sequences (end gauche versus GTG0) in alkanes, Ramanmeasurements provide a direct measurement of ‘‘melted’’ chainsegments through the disordered mass fraction.

Conclusions

Analysis of the Raman spectra over a range of alkane lengthsemphasizes the appearance of non-crystalline trans chain segmentsprior to the melt transition. These NCCT conformers comprise amajority mass fraction when the alkane is in a rotator phase, whichdecreases with increasing temperature and chain length. Longeralkane chains with no rotator transition produce smaller amountsof NCCT on predominantly crystalline chains prior to the crystal–melt transition. This quantification of NCCT and gauche-richfractions compliments the observation of specific gauche–transsequences that can be observed in IR measurements. DFTcalculations of the Raman spectra of a C21 alkane with gauchebonds placed sequentially along the chain reveal that thedisordered mass fraction can contain a small fraction of con-formationally disordered bonds along primarily trans segments.In contrast, the NCCT conformers are comprised of transsequences devoid of any gauche conformers. We expect thatour interpretation and analysis of the Raman spectra of alkanescan be generalized to provide structural information on crystal-line molecules with long alkane segments: saturated long-chainalcohols, fatty acids, etc. The Raman measurement also allowsfor time-dependent characterization of chain conformers duringphase transitions between the melt, rotator, and crystallinephases. More directly, the analysis of melting alkanes bettercharacterize the NCCT mass fraction observed during polyethylenecrystallization, which is critical to understanding the role of NCCTconformers in polyethylene processing.

Appendix: DFT spectra calculations

Calculations of the Raman spectra are performed using theGaussian 09 (Gaussian, Inc.) suite of programs.46 Geometryoptimization to local minima and frequency calculations are

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performed at the DFT level using the B3LYP functional and the6-31G(d,p) basis set. The convergence criteria for geometryoptimization are a maximum force of 4.5 � 10�4 Hartree anda maximum root mean squared force of 3 � 10�4 Hartree perBohr. The initial dihedral angles of the alkane for trans andgauche bonds are 1801 and �601, and no constraints are used tofix the alkane geometry. The Raman scattering intensity iscalculated based on the calculated Raman scattering activityand an assumed Lorentzian peak shape with 2 cm�1 peak widthfor each vibrational mode. To directly relate the calculatedspectra to experimental results, we have scaled the calculatedRaman shift in the CH2 twist region by 0.975 for all cases.

Calculations of the Raman spectra are performed for the C21

alkane with either a single gauche bond or GTG0 sequence onthe chain, and characteristic Raman scattering activities andintensities in the CH2 twist region are shown in Fig. 7. The typeand position of a sequence is indicated by the abbreviationTa(G or GTG0)Tb, where the subscripts a and b indicate thenumber of consecutive trans bonds (T). The alkane consistingof all trans bonds T18 shows a vibration at the consecutive transCH2 twist position with a strong Raman scattering activitysurrounded by vibrational modes of lesser Raman activity,which leads to a single large peak in the scattering intensitywith a small shoulder near 1303 cm�1. When a single gauchebond is present on the chain, a greater number of vibrational

modes appear in the spectra, especially for Raman shift valuesin the region corresponding to the amorphous CH2 twist mode. Agauche bond near the center of the molecule as in T8GT9 generates anumber of Raman active modes near the consecutive trans peak thatare indistinguishable from a single peak. A qualitatively similar effectis seen for GTG0 sequences at various positions in Fig. 7.

The calculated spectra in Fig. 7 indicate that the presence ofgauche bonds increase the scattering intensity in the amorphousregion, which we expect to decrease the integrated intensityof the trans CH2 twist peak relative to the integrated intensity ofthe same peak in the spectra of the all trans C21 alkane. To relatethe calculated spectra to our measurements in the Resultssection, we must estimate the mass fractions of amorphousand consecutive trans conformers from the calculated scatteringintensities shown in Fig. 7. Since the calculated spectra containmultiple peaks in the CH2 twist region instead of the twosmooth peaks observed in the experimental spectra, we estimatethe calculated consecutive trans mass fraction ac

ct by the ratioof the scattering intensity of the trans CH2 twist vibrationh(1296 cm�1) of the alkane with a single gauche bond tothe scattering intensity hT(1296 cm�1) of the T18 chain: ac

ct =h(1296 cm�1)/hT(1296 cm�1). The calculated disordered massfraction from conservation of mass arguments is ac

am = 1 � acct.

Disclaimer

Certain commercial equipment, instruments, or materials areidentified in this paper in order to adequately specify experimentalprocedure. Such identification does not imply recommendation orendorsement by the National Institute of Standards and Technology,nor does it imply that the materials or equipment identified arenecessarily the best available for the purpose.

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