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Nuclear Magnetic Resonance Experiments and Molecular JOURNAL OF CHEMICAL PHYSICS VOLUME 116, NUMBER 18 8 MAY 2002 Segmental dynamics in a blend of alkanes: Nuclear magnetic resonance experiments and molecular dynamics simulation Joanne Budzien Department of Chemical Engineering, University of Wisconsin–Madison, Madison, Wisconsin 53706 Colleen Raphael and Mark D. Ediger Department of Chemistry, University of Wisconsin–Madison, Madison, Wisconsin 53706 Juan J. de Pablo Department of Chemical Engineering, University of Wisconsin–Madison, Madison, Wisconsin 53706 ͑Received 7 December 2001; accepted 4 February 2002͒ The segmental dynamics of a model miscible blend, C24H50 and C6D14 , were investigated as a function of temperature and composition. The segmental dynamics of the C24H50 component were 13 measured with C nuclear magnetic resonance T1 and nuclear Overhauser effect measurements, 2 while H T1 measurements were utilized for the C6D14 component. Use of low molecular weight alkanes provides a monodisperse system in both components and allows differentiation of dynamics near the chain ends. From these measurements, correlation times can be calculated for the C–H and C–D bond reorientation as a function of component, position along the chain backbone, temperature, and composition. At 337 K, the segmental dynamics of both molecules change by a factor of 2 to 4 across the composition range, with the central C–H vectors of tetracosane showing a stronger composition dependence than other C–H or C–D vectors. Molecular simulations in the canonical and isobaric–isothermal ensembles were conducted with a united-atom force field that is known to reproduce the thermodynamic properties of pure alkanes and their mixtures with good accuracy. With a minor change to the torsion parameters, the correlation times for pure tetracosane are in good agreement with experiment. For pure hexane and its mixtures with tetracosane, the simulated dynamics are faster than experiment. © 2002 American Institute of Physics. ͓DOI: 10.1063/1.1464538͔ INTRODUCTION multaneously. This postulate, however, was proposed before the availability of more accurate UA models for thermody- Molecular simulations have been shown to be capable of namic properties.1,2 predicting the structure and thermodynamic properties of Several studies have examined the performance of UA relatively complex fluids, including alkanes and polyolefins. models vis-a`-vis that of AA models for prediction of dy- Not as much is known about the ability of available force namic properties.4,6–8 Simulations were performed for fields to reproduce the dynamic properties of such fluids. In n-tridecane, n-tetratetracontane, and n-C100H202 ; results of this work we investigate whether a force field previously UA and AA models were compared to experimental data for optimized for thermodynamic properties of alkanes and their various dynamic properties, including C–H bond orientation mixtures can also provide an accurate description of dynam- correlation times and diffusion coefficients. It was found ics in these systems. that, in general, the UA results were worse for dynamic prop- Simulations of alkanes can be performed at varying lev- erties than would be expected from static-property results. els of molecular detail. At the most detailed level, all-atom Anisotropic-united-atom models are generally perceived ͑AA͒ force fields consider each atom individually. At a to offer an attractive alternative to AA models for simula- slightly more coarse-grained level, united-atom ͑UA͒, and tions of alkanes or polyolefins. Simulations using an AUA anisotropic-united-atom ͑AUA͒ force fields treat carbon at- model, for example, have been shown to provide a good oms and their bonded hydrogens as a single interaction site. description of the equation of state and the heat of vaporiza- The UA model considers forces to act on the center of the tion of polyethylene.5 More recent calculations using the site, while the AUA model displaces the acting forces from same force field indicate that good agreement with experi- the center of the site. For a simple alkane, the computational ment can be achieved for the dipole relaxation time as a demands of a simulation with a UA force field are consider- function of both temperature and pressure.9 ably smaller than those of an all-atom calculation. That In a recent series of papers, a group of researchers3,10–13 higher computational efficiency has fostered the recent de- have compared the performance of UA and AUA models. velopment of simple force fields capable of describing the The results have been mixed, and obscured by the use of thermodynamic properties of alkanes and polyolefins.1–3 It combinations of different UA force fields, some of which are has been postulated that UA models are not able4,5 to de- known to be inaccurate. While this body of work suggests scribe thermodynamic and dynamic properties of alkanes si- that AUA models are superior, these conclusions could be 0021-9606/2002/116(18)/8209/9/$19.008209 © 2002 American Institute of Physics Downloaded 05 Mar 2007 to 128.104.198.71. Redistribution subject to AIP license or copyright, see http://jcp.aip.org/jcp/copyright.jsp 8210 J. Chem. Phys., Vol. 116, No. 18, 8 May 2002 Budzien et al. partly based on inappropriate comparisons. Simulations by a Deuterated hexane dynamics different group of researchers14–17 comparing UA and AUA Because 2H nuclei relax via the quadrupolar mechanism, models did not reveal any clear advantages for dynamic the relationship between T and J(␻)is properties of one over the other; each force field had strong 1 points. 1 3 e2qQ 2 ϭ ␲2ͩ ͪ ͓ ͑␻ ͒ϩ ͑ ␻ ͔͒ ͑ ͒ J D 4J 2 D . 4 A review of the literature suggests that simulations of T1 10 h dynamic properties using some of the more recent and accu- All the 2H experiments reported here are in the extreme rate UA force fields have been scarce. In this study, a series narrowing limit. In this case, the spectral density function is of NMR experiments were performed for systems of hexane, equal to its zero frequency limit and there exists an inverse tetracosane, and their mixtures, to quantify fast dynamic pro- relationship between the correlation time ␶ and T : cesses as a function of temperature, composition, and field c 1 strength. Molecular dynamics simulations of the same sys- 1 3 e2qQ 2 ϭ ␲2ͩ ͪ ␶ ͑ ͒ tems were then conducted using the NERD UA force field, c . 5 T1 2 h which has been shown to reproduce the thermodynamic 2 2 properties ͑including phase behavior͒ of alkanes with good For C6D14 , the quadrupole coupling constant (e qQ/h) ␣ accuracy.1,18 Our results suggest that united-atom force fields is equal to 168 KHz for deuterons attached to the carbon ͑ ͒ ␤ ␥ are capable of describing simultaneously the equilibrium methyl groups and 172 KHz for the and deuterons. The ␣ thermodynamic properties and several dynamic aspects of deuterons are detectable as one peak in the spectrum while ␤ ␥ intermediate to long alkanes. the and deuterons are detectable as a second peak. EXPERIMENTAL METHODS AND DATA ANALYSIS Tetracosane dynamics Tetracosane (C H ) was purchased from Aldrich and 24 50 Five peaks are resolved in the 13C NMR spectrum of used as received. Perdeuterated n-hexane (C D ) was pur- 6 14 C H , corresponding to the four carbons at each end of the chased from Cambridge Isotope and used as received. 24 50 chain ͑␣ϭmethyl, ␤, ␥, ␦͒ and the 16 carbons in the center of Samples were made with the following mass fractions of the chain. Hence the dynamics of five types of C–H vectors C H : 100%, 86%, 50%, 10%, and 0%. Freeze–pump– 24 50 can be investigated. Dipole–dipole ͑DD͒ interactions are the thaw cycles were used to eliminate oxygen from the samples. 13 main relaxation mechanism for these experiments. In some C NMR T1 and NOE experiments were performed on the 13 13 cases, spin rotation ͑SR͒ also plays a role. The observed C C24H50 components of the mixtures at C Larmor frequen- 2 relaxation rate can be expressed cies of 125.8, 75.5, and/or 62.9 MHz. H T1 experiments were carried out on the C D components of the mixtures at 1 1 1 6 14 ϭ ϩ ͑ ͒ 2H resonance frequencies of 76.9 and/or 55.3 MHz. The tem- DD SR . 6 T1 T1 T1 perature ranges of the experiments were chosen to ensure that the samples would be in the one-phase region for all The separation of the measured T1 into its two compo- ͑ DD SR͒ measurements. Temperatures were calibrated against the eth- nents T1 and T1 can be accomplished using the experi- 19 mentally measured nuclear Overhauser effect ͑NOE͒ values. ylene glycol spectrum. For the pure C6D14 sample, it was necessary to use an NMR tube with a small inside diameter The NOE value associated with dipole–dipole interaction DD ͑2mm͒ in order to eliminate convection.20 NOE is bounded below by the observed NOE and above by 2.99. NOEDD should increase or remain constant as the NMR observables temperature increases, as the concentration of C24H50 de- The connection between NMR observables and molecu- creases, as the resonance frequency decreases, and as the end lar motion is made through the orientation autocorrelation of the chain is approached. Most of our data showed these function G(t) for a 13C–H or C–2H vector. If the orientation trends; in these cases, we set NOEDD equal to the observed DD of this vector is designated as ex , this time correlation func- NOE and T1 equal to the observed T1 . When the data did tion can be written not show these trends, NOEDD was estimated using the above expectations, and the TDD was calculated from ͑ ͒ϭ 1͗ ͑ ͑ ͒ ͑ ͒͒2Ϫ ͘ ͑ ͒ 1 G t 2 3 ex 0 •ex t 1 , 1 ͓NOEDDϪ1͔ where the brackets indicate an average over all possible start- DDϭͩ ͪ ͑ ͒ T1 ͓ Ϫ ͔ *T1 .
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