J. Phys. Chem. 1994,98, 11739-11744
11739
Gauche Defects, Positional Disorder, Dislocations, and Slip Planes in Crystals of Long Methylene Sequences G. L. Liang, D. W. Noid, B. G. Sumpter, and B. Wunderlich’ Chemical and Analytical Sciences Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831-6197, and Department of Chemistry, The University of Tennessee, Knoxville, Tennessee 37996-1600 Received: February 24, 1994; In Final Form: June 21, 1994@
Conformational disorder in crystals of long methylene sequences in the form of gauche defects has been studied in the last few years in our laboratory by using large-scale molecular dynamics stimulations. The distribution of gauche defects within crystals simulated under different conditions and temperatures has been extracted and is shown to depend mainly on temperature and to some degree on external constraints. The crystal surfaces, and especially those that contain chain ends, have a higher probability for conformational disorder. The results supplement available experimental data and provide atomistic details about this dynamic disorder. Plastic deformation could be produced by letting a compressed crystal expand in one direction. Positional disorder, dislocations, and slip planes were produced in this process and are detailed.
Introduction The understanding of structure and dynamic properties of ordered assemblies of hydrocarbon chains is ultimately based on our knowledge about their defects. Of the defects, conformational disorder is unique in its disruption of packing and increase of large-amplitude motion without breaking of chemical bonding.’ The common conformational defect is a gauche conformation, interrupting a sequence of ordered trans conformations (t). A gauche conformation is caused by an approximately 120” rotation about the backbone bond in the positive or negative directions (gf or g-). These defects are of importance in polymer crystals,2 mesophases (such as liquid crystals, plastic crystals, or condis crystal^),^ and biological materials (such as biomembranes formed of lipid bilayer^).^ Early proposals linked motion of such defects to chain diffusion in crystals.’ The main experimental technique to measure the gauche concentration is by vibrational spectroscopy. Zerbi et aL5 analyzed solid n-nonadecane (C19&) via IR and Raman spectroscopy using, in addition, selectively deuterated samples. Their quantitative analysis was based on the shifts in selected vibration frequencies caused by gauche defects. Normal mode calculations of the frequency spectra for guidance of the interpretation were based on a force field derived by Snyder.6 The first results suggested that all gauche defects were in the bonds between carbon atoms 2 and 3 from the end (end gauche defects). The studied crystal phase was the hexagonal “rotator phase”. Double-gauche defects (g+g+ or g-g-) and kinks (g+t-g- sequences, written as 2gl kink) were not dete~ted.~ Somewhat different conclusions were reached by Snyder et aL7 who studied conformational disorder and solid-solid phase transitions in n-alkanes from C17H36 to CaH122. They found that gauche bonds exist also in the interior of the crystals and double-gauche sequences and kinks are also possible. Selective deuteration also allowed the determination of the distribution of gauche bonds along the chain. The probability of gauche bonds was found to increase exponentially toward the chain ends7 These results of Snyder et al. have since been used as a reference for the determination of gauche-bond concentrations @
Abstract published in Advance ACS Abstracts, October 15, 1994.
0022-365419412098- 11739$04.50/0
by other techniques, such as solid-state NMR.8 In this paper these conclusions will be supported and additional molecular details will be supplied by using molecular dynamics simulations. It is well-known that dislocations and slip planes govern the deformation of metals, salts, and other crystals that are strongly bonded in three dimensions. Such one- and two-dimensional defects were also considered for crystals of flexible macromolecules.* These defects were, however, found to be limited in their contribution to deformation mechanisms because of the permanent covalent bonding along the backbone chain of the molecules. A general discussion of this topic can be found in refs 1 and 2. Edge dislocations were observed by electron microscopy but found to be largely sessile and without a continuous source to feed major deformation processes. Along slip planes easy motion of dislocations is possible, permitting plastic deformation of the crystals. In polymer crystals such slip planes are limited to crystallographic planes that do not cut across the molecular chains and are, in addition, restricted by chain folds and entanglements at the crystal surfaces. Screw dislocations with very large Burgers vectors are seen frequently in polymer crystals and paraffins. They are usually of the size of the crystal thickness and are commonly instrumental in crystal growth but are not involved in deformation. The major deformation process in polymeric materials is the industrially important drawing of fibers and films. Little is known about the molecular details during these rather chaotic processes. Molecular dynamics (MD) simulations can provide the extreme, picosecond slow-motion representation of molecular motion, needed to study the dynamics, properties, and distribution of disorder (1 ps = 10-l2 s). Full MD simulations of sufficiently large paraffin crystals to serve as a model to the microcrystalline polymers became possible in our laboratory for crystals of up to 227 nm3.9 In this paper we report on new analyses of the concentrations and distributions of gauche conformations, as well as on the positional disorder, dislocations, and slip planes observed during plastic deformation of partially constrained crystals. The analyses are based on trajectories generated during earlier simulations that were carried out by using several thousand hours of supercomputer time. 0 1994 American Chemical Society
11740 J. Phys. Chem., Vol. 98, No. 45, 1994
Liang et al.
Projection of a 192-Chain MONO Crystal along the z-Axes [The crysta11ogra phi c a. b (chain), and c -_directions are parallel to x, z, and y] 1-0
2.0t
(The shaded area can be restrained in experiments to show pl~sticdeformation)
-3.0
Figure 1. Crystal structures of pentacontamethylene before the beginning of the simulation in x-y projections (along z, the chain axis). The pairs of crosses indicate the centers of the CH2 groups of the alltrans zigzag chains of the monoclinic (MONO) crystal structure. Simulation Technique and Results The basic model crystal contained 192 chains of pentacontamethylene (CsoHlm). The chains were initially placed on positions determined by the orthorhombic (0RTH)'O and monoclinic (MONO)' polyethylene crystal structures, as measured by X-ray diffraction at room temperature (ORTH, a = 0.74, b = 0.49, c = 0.25 nm with c being the chain axis; MONO, a = 0.81, b = 0.25, c = 0.48 nm, and /?= 108" with b being the chain axis). The chain axes were chosen to be parallel to the z axis of Cartesian coordinates, as shown in Figure 1 for the MONO example. For a study of the effect of constraints on the conformational disorder and its distribution, two, three, or all of the four side surfaces of the crystal were held in fixed position as rigid but interacting atoms. Figure 1 shows the example of a three-side constraint, of interest for the plastic deformation to be described. The simulations used both united-atom (UA) and full-atom (FA) models. In the UA simulation a CH2 group is represented by a single center of mass; in the FA simulation all atoms are accounted for. Stretching, bending, and torsion were considered for the dynamic chains. All dynamic and rigid atoms contributed to the van der Waals, weak interactions. For the UA model, we used the force-field parameters of ref 9. For the FA model, the parameters of Barnes and Fanconi'* were employed, as is described in detail in ref 13. The advanced programming strategies for our MD codes permit these large simulations to times as long as 100 ps. The details have been described in ref
14. The simulations were carried out on the Cray X-MP computer at Oak Ridge National Laboratory and the IBM 3090 and V A X 9OOO computers at the University of Tennessee at Knoxville, requiring a total of about 1500, 1O00, and 2400 h of CPU time, respectively. The conformational disorder and its distribution was extracted from 16 simulations with different constraints and at various temperatures, as listed in Table 1. The D-series represents unconstrained UA simulations. The S-series consists of surfaceconstrained UA simulations with the type of constraint listed in column four. The four-sided constraint (4-SC) has all surface chains static but permits diffusion in the chain direction. In the three-sided constraint (3-SC) one of the x-z planes is mobile, as shown in Figure 1. The two-sided constraint (2-SC) keeps one x-z and one y-z surface mobile. The x-y surface with its chain ends remains unconstrained in all simulations. The X-series, finally, refers to unconstrained FA simulations. The nonbonding interactions were cut off at 1.0 nm in the neighbor list generated during the simulation. To start the simulation, a certain amount of momentum, selected by a random number generator, was distributed among all atoms. The velocities of the atoms reached a Boltzmann distribution within about 0.2 ps. The trajectories were calculated every 0.05 ps for UA simulations and 0.01 ps for FA simulations, using an ordinary differential equation solver. The torsional angle of every set of four connective carbons was calculated each picosecond. If the angle deviated from that of the all-trans conformation by more than 90°, it was considered to be a gauche bond. The concentration of gauche bonds was then extracted from the trajectories. The lifetime of most gauche bonds was less than 10 ps and the gauche concentration fluctuated with time. In Table 1, g, the initial steady-state concentration of gauche bonds in the entire crystal is given as percent of the total number of gauche bonds possible. To judge the location of the gauche bonds within the crystal, the following information was extracted from the extensive defect maps generated: The percentage of the gauche bonds that are located in the first two layers of dynamic chains in the xz and yz surfaces is given by g/g in percent of g. The number of sequential double gauche bonds is given by gg, and k is the number of kinks. Since the concentrations of double-gauche bonds and kinks are low, their values are expressed in absolute numbers. For reference, there are 9024 bonds about which conformational isomers can occur
TABLE 1: Concentrations of Conformational Defects in Different Cwstals series no. Do3 M)4
Do5
Do8 Do9 D10 s10 s11 s12 S13 S14 S15 x02 X04 X05 X06
time, ps 10 25 100 10 10 100 20 100 100 33 66 15 10 10 10 6
cryst type ORTH ORTH ORTH MONO MONO MONO MONO MONO MONO ORTH ORTH ORTH ORTH ORTH ORTH ORTH
constraint type none none none none none none 4-sc 3-sc 3-sc 3-sc 4-sc 2-sc none none none none
temp: K 229 318 409 236 330 40 1 405 402 227 410 333 383 247 312 371 434
g," %
g/g,b no.
0.06
-
0.43 1.93 0.03 0.43 1.84 1.06 1.10 0.02 1.11 0.32 1.17 0.04 0.6 1 1.78 4.18
56 56 65 63 68 62 74
-
49 52 51
gg," no.
0 5
13 1 2 16 8 9 0 5
k," no. 0 4 19 0 3 15 4 6 0
-
2 8
11 3 8
0
0
76 83 72
10 21 38
11 62 142
Figure 4 a b C
d e f g
h i j
k 1
m n 0
P
Temp is the temperature of the system when the maximum concentration of gauche conformations is reached. g represents the initial gauche concentration in the crystal at the given temperature, g/g the percentage of these gauche bonds that resides in the two mobile outermost layers of the crystal, gg is the number of sequential gauche bonds, and k the number of kinks (gauche-frans-gauche sequences). The gauche bonds at the chain ends can be gained from the corresponding part of Figure 4. - indicates a too small gauche concentration to evaluate gig.
J. Phys. Chem., Vol. 98,No. 45,1994 11741
Crystals of Long Methylene Sequences I
1
I
I
I
-4 Gauche Concentration (in %)
t3 100
150
200
250
300
Temperature
350
400
450
(K)
Figure 2. Concentration of gauche conformations as a function of temperature for all simulations listed in Table 1 after attainment of the steady state. The points that collect in the lower curve originate mainly from the unrestrained MONO crystals (D-series) and all restrained crystals (S-series).
Formation of Defects in Polyethylene
. .-
I.,
,
Figure 3. Conformation of the lower part of a surface chain of a polyethylene crystal as function of time, showing the development of a kink (2gl). The insert shows seven neighboring chains at higher temperature with larger vibrational de~iati0ns.l~
in each fully dynamic crystal and correspondingly less in the constrained crystals of series S . During the course of the simulation, the gauche concentration reaches an initial steady state after about 5-10 ps, at the approximate temperature given in the table. At longer simulations times the temperature of the crystal drops due to energy losses caused by limits in the computation precision and, as a result, the gauche concentration decreases. This decrease in temperature is only 1-3 Wps, so that steady state, once attained, is kept for the full simulation, and a large number of concentration values can be extracted for a broad range of temperatures. The change of gauche concentration with temperature is shown in Figure 2 for all steady-state data of the simulations of Table I. All types of conformational defects are generated as a result of interactive thermal motion. A typical mechanism of formation of a kink is reproduced in Figure 3. It shows the combination of transverse, torsional, and longitudinal skeletal vibrations necessary to generate the kink. Once created, this particular kink had a lifetime of about 2.5 ps. The kink of Figure 3 was formed on the surface of a smaller crystal than the ones simulated in the series of Table l . I 5 To study the distribution of conformational disorder, the position of each gauche bond within the defect map was identified by a three-dimensional matrix index of which ix and iy fix the chain along the x and y directions as shown in Figure 1. The index iz, with values from 1 to 47 for the possible bonds that can rotate to a gauche conformation, locates the position of the defect along the chain (from the bottom to the top). Conformational disorder was found in practically every mobile
chain, but the surface chains are more likely to have gauche bonds than the chains in the interior of the crystal. The values g/g in Table 1 indicate that in all unconstrained crystals the majority of gauche bonds exist in the surface chains. The simulations D03, S12, and X02 are at such low temperatures that they have insufficient gauche bonds to give reliable estimates of the partition of the defects. The distributions of conformational disorder along the chain axes are shown in Figure 4. The histograms cover all gauche conformations detected during the entire simulation time (Le., over the full range of decreasing temperature). The plastic deformation was followed in simulation S 11 of Table 1. By starting the crystal on positions in equilibrium at about room temperature, one can estimate that in this simulation the instantaneous temperature increase to about 400 K causes a pressure increase of 250-500 MPa, forcing the chains to move laterally out of the enclosure that is indicated by the shaded area of Figure 1.16 Figure 5 illustrates the change in the x and y coordinates of the centers of gravity of the dynamic chains at time steps from 2 to 8 ps. The deformation starts at 2 ps with a buckling of the mobile x-z surface and has reached its maximum deformation at about 8 ps. At later times the temperature drops sufficiently to have the crystal shrink to its initial density, but it keeps its irregular shape, as can be seen from the time squence of the positions of the chains in the top layer, shown in Figure 6. A more detailed discussion of the density variation in this and the other simulations of constrained crystals can be found in ref 17.
Discussion Gauche Concentration and Distribution. The overall gauche concentrations of Table 1 and the extended data of Figure 2 match the limited experimental data within the rather large uncertainty of the e~periment.~ Using the data of ref 7c, one can estimate values for the total gauche concentration for C50H102 of 0.2% at 300 K, 0.6% at 360 K, and 1.7% at the melting temperature 365.2 K. These values are close to the curve for C5oHloo of Figure 2. The upper and lower branches of the points in Figure 2 contain for the unconstrained series of simulations D predominantly the data from originally ORTH and MONO crystals, respectively. These differences, although close to the general spread, occur despite the fact that in the unconstrained crystals the resulting hexagonal structure has the same radial distribution function for all initial structure^.^^ One expects, thus, that the setting angle of the zigzag chains may need close attention for a detailed discussion of the mechanism of formation of conformational disorder. The differences between the gauche concentrations of constrained, unconstrained, and between the united atom (UA) and the full atom (FA) simulations are not any larger, although it may be significant to note that all constrained simulations S tend to the MONO crystals of the unconstrained crystals of series D (see also Table 1). The restrictions of the crystal structure and external strain cause thus only a minor change in the overall gauche concentration. This observation agrees with the experimental observation that paraffins in the lower density hexagonal rotator phase and in the orthorhombic or monoclinic crystal phase have similar overall gauche concentration^.^,^ The distribution of conformational disorder along the z axis is shown in Figure 4 for the temperatures listed in Table 1. In the unconstrained UA simulations (D-series, Figure 4a-0, all distributions are similar at similar temperatures (compare parts a to d, b to e, and c to f i n Figure 4). At low temperatures, the concentrations of gauche bonds are small and only a few discrete
Liang et al.
11742 J. Phys. Chem., Vol. 98, No. 45, 1994 60 40
20
20
IO
0
-
E 200
0
50
0
.5a4 0 0 a
0
50
iz
iz
50 it
(h)
I
60 40
20 0
I50
(i)
1
50
50
iz
IZ
it.
IZ
1 -
I 50
80
60 40
20 0
50
25
(k)
I
80
(1)
I
20
,E
e
.s-
15
3n
a
a IO
150
I50
100
3 100
2
d:
5 0
s
8 50
50 0
50
50
iz
50
iz
iz
50
iz
iz
0
50
it
Figure 4. Histograms of the numbers of gauche conformations that appeared at the indicated positions ix along the chains (summed over all mobile chains and the full simulation duration of the given crystal, Le., covering a temperature range that is determined by the initial temperature and the simulation time): (a) DO3; (b) DO4; (c) DO5; (d) DO8; (e) DO9; (0D10; (g) S10; (h) S11; (i) S12; (i)S13; (k) S14; (1) S15; (m) XO2; (n) Xo4; ( 0 ) XO5; (p) X06.
Plastic Flow of C5*H1 oo -Chains
*tal
Structure:
monoclinic b = chain direction = t
(in nm)
scale in the x-Direction (nm)
Figure 5. Changes of the dynamic chains in simulation S11 of Table 1 during the plastic deformation in a three-side constraint as shown in Figure 1. The heavy lines connecting the positions of the center of gravity of the chains indicate original nearest neighbors. The thin lines in the 8-ps picture indicate the new (001) lattice planes and the (102) slip plane. The edge dislocation vector is located at 1. gauche bonds are found with seemingly little preference of position (parts a and d of Figure 4). As the temperature increases (parts c and f of Figure 4), the distributions from
Figure 6. Time dependence of the motion of the top layer of the simulation S11, shown in Figure 5. The dotted line matches the crystal positions of the retaining rigid chains (see Figure 1). positions iz = 5 to iz = 42 level out. These curves are quite similar to the distributions of gauche bonds derived from deuterium-substituted paraffins.' It is interesting to note that in all D-series simulations, most gauche bonds in the iz positions between 5 and 42 are, in addition, located in chains close to the xz and yz surfaces of the crystals. This means that not only
J. Phys. Chem., Vol. 98, No. 45, 1994 11743
Crystals of Long Methylene Sequences are gauche conformations preferentially in the side surfaces but, of the ones in the center chains, most are also near the top and bottom surfaces. Turning to the simulations of the constrained crystals, the S-series, one finds the g and g/g values in Table I, as well as the distributions along z, given in Figure 4g-1, to be similar to the unconstrained D-series. The interior chains have, however, similar distributions along z as the surface chains, in contrast to the D-series. The distribution of gauche bonds in the S-series depends also somewhat on the initial crystal structure and type of constraint. This was to be expected since the constrained simulations that started from a MONO structure retained largely the MONO structure, while the initially ORTH crystals changed to a new structure with chains in the position of the ORTH structure, but with parallel chains.I6 At the same initial temperature, a higher number of gauche conformations can be seen at the ends and less in the center for MONO crystals (compare parts h and j of Figure 4). Over similar temperature ranges, four- and three-side constraints seem to have similar distributions, as shown in Figure 4g, and h (note the difference in simulation time). The difference between MONO and ORTH crystals seems also present with four-sided constraint (compare Figure 4g,k) (note the differences in temperature). In the unconstrained, short simulations including all H-atoms (FA, X-series, Figure 4m-p), the exponential increase of gauche-bonds toward the chain ends is already well established for all temperatures, despite the short simulation times. In contrast to the UA simulations,the explicit hydrogen interactions seem to decrease the formation of gauche bonds in the middle of a chain. The simulations reveal several different effects of the crystal environment on the distributions of gauche conformations. An unconstrained crystal surface enhances defect formation, as expected. On such surfaces there is no steric hindrance due to neighboring chains, and the only energetics opposing disordering are intramolecular and the adhesion to the surface. For surface-constrained crystals, more gauche conformations are found in the center of the crystal (see also Table 1). A possible reason for this effect is the position of the nodes of the volume breathing modes of vibration of the crystal. With surface constraint higher vibration amplitudes occur in the center, without, on the surface. On this basis one may speculate that there should also be a dependence of defect formation on crystal or domain size. This observation may even furnish an explanation for the different experimental findings of no or some defects in the center of the chain summarized in the Introduction. In addition to the obvious possibility of different experimental sensitivities, there may have been different sample preparations in the different re~earches.~,’ The general observation of higher gauche conformations at the chain ends is connected with the ease of longitudinal diffusion of the chains. Once the chain escapes the crystal environment, only intramolecular forces try to keep the chain in its trans conformation. With increasing temperature, an increasing surface roughness develops due to this diffusion of the chains parallel to z . ~More details about the mechanism of longitudinal diffusion of the chains under external forces were given in ref 15. The motions of chains to relieve the intemal pressure in the four-sided constraint simulations (runs S10 and S14) are given in ref 16. Positional Disorder, Dislocations, and Slip Planes. The plastic deformation, simulated in Figure 5 , documents lateral displacement of polymer chains by a mechanism that is not much different from similar deformations of crystals of small motifs like metals, salts, and ceramics. The picture of the
dynamic chains after 8 ps clearly demonstrates an overall slip along the crystallographic (102) plane. Along this plane the major deformation of the crystal occurred, involving mobile edge dislocations. The motion of these dislocations is restricted, as discussed in the Introduction, by the directiveness of the strong bonds along the z-direction. The strong buckling along the slip plane produces considerable positional disorder. Drawing approximate (001) planes through the crystal illustrates the expulsion of the four neighboring top chains and the creation of a shorter layer using two or three chains of the next lower (001) plane. This continues with one chain of layer three from the top. To accommodate the extra chains in the interior of the cavity, an edge dislocation can be seen at the marked position. The time sequence in Figure 6 permits a detailed kinetic analysis of the plastic deformation. At the later simulation times (23 and 70 ps) the temperature has dropped to and below room temperature. The new surface produced between 5 and 8 ps does, however, not recover its most stable position. The small crosses in the figure mark adjacent crystal positions derived from the initial lattice parameters. From this first MD simulation of plastic deformation of a crystal of chain molecules, one can see that much shorter times than commonly assumed are necessary to yield valuable mechanistic information. The largeamplitude molecular motion that underlies macroscopic deformation has a basic picosecond timescale and is slowed only by the large number of cooperative steps needed to result in macroscopic displacements.
Conclusions A reexamination of a large number of MD trajectroies has shown that such simulations can duplicate experimental results on the temperature dependence of conformational defects and has given additional information on their distribution. The simulations suggest that there is some dependence of the defect distribution on local constraints, such as crystal structure, size, and external constraints. In general, the conformational disorder is concentrated in surface areas. Plastic deformation could for the first time be visualized realistically. Despite the short time available for the simulation, it seems that no other processes need to be invoked to understand the macroscopic deformation. These findings should be also of importance for the description of, for example, polymer mesophases and lipid bilayers, where the hydrocarbon assemblies are subject to different constraints. The MD simulations can extend experiments by providing atomistic details of defect formation and distribution. Similar results could serve as a model for the study of systems of molecular assemblies such as Langmuir-Blodgett films and biomembranes that can also have special application in electrical, optical, magnetical, and other field-effect devices.
Acknowledgment. This work was supported by the Division of Materials Sciences, Office of Basic Energy Sciences, U.S. Department of Energy, under Contract DE-AC05-840R21400 with Martin Marietta Energy Systems, Inc., and the Division of Materials and Research, National Science Foundation, Polymers Program, Grant DMR 92-00520. The Chancellor of The University of Tennessee and the University Computing Center are acknowledged for providing computing facilities and services. References and Notes (1) Sumpter, B. G.;Noid, D. W.; Liang, G. L.; Wunderlich, B. Atomistic Dynamics of Macromolecular Crystals; Springer Verlag: Berlin, 1994 (Adv. Polym. Sei. 1994, 116, 21-12; volume on Atomistic Modelling of Physical Properties of Polymers).
11744 J. Phys. Chem., Vol. 98, No. 45, I994 (2) Wunderlich, B. Macromolecular Physics; Academic Press: New York, 1973, 1976, 1980; Vols. I-III. (3) Wunderlich, B.; Grebowicz, J. Adv. Polym. Sei. 1984, 60/61, 1. Wunderlich, B.; Moller, M.; Grebowicz, J.; Baur, H. Conformational Motion and Disorder in Low and High Molecular Mass Crystals; SpringerVerlag: Berlin, 1988 (Adv. Polym. Sei. 1988, 87). (4) Small, D. M. In The Physical Chemistry of Lipids: from Alkanes to Phospholipids. Handbook of Lipid Research;Hanahan, D. J., Ed.; Plenum Press: New York, 1986. ( 5 ) Zerbi, G.; Magni, R.; Gaussoni, M.; Moritz, K. H.; Bigotto, A.; Sirlikov, S. J . Chem. Phys. 1981, 75, 3175. (6) Snyder, R. G. J . Chem. Phys. 1967,47, 1316. (7) Snyder, R. G.;Maroncelli, M.; Qi, S. P.; Strauss, H. L. Science 1981, 214, 188. Maroncelli, M.; Strauss, H. L.; Snyder, R. G. J. Chem. Phvs. 1985. 82. 2811. Kim. Y.: Strauss. H. L.: Snvder. R. G. J. Phvs. Ciem. 1989, 93, 7520. (8) Moller. M.: Cantow, H.-J.; Drotloff, H.; Emeis, D.; Lee, K.-S.; Wegner, G. Makromol. Chem. 1986, 187, 1237.
Liang et al. (9) Liang, G. L.; Noid, D. W.; Sumpter, B. G.;Wunderlich, B. Makromol. Chem., Theory Simul. 1993,2,245; Acta Polym. 1993,44,219; J. Polym. Sci.: Part E : Polym. Phys. 1993, 31, 1909. (IO) Bunn, C. W. Trans. Faraday SOC. 1939, 35, 482. (11) Seto, T.; Hara, T.; Tanaka, K. Jpn. J. Appl. Phys. 1968, 7, 31. (12) Barnes, J.; Fanconi, B. J . Phys. Chem. Ref. Dafa 1978, 7, 1309. (13) Liang, G.L.; Noid, D. W.; Sumpter, B. G.; Wunderlich, B. Comp. Polym. Sei. 1993, 3, 101. (14) Noid, D. W.; Sumpter, B. G.; Wunderlich, B.; Pfeffer, G. A. J. Comp. Chem. 1990, 11, 236. Noid, D. W.; Sumpter, B. G.; Cox, R. L. J . Comp. Polym. Sei. 1991, I , 161. (15) Sumpter, B. G.; Noid, D. W.; Wunderlich, B. Macromolecules 1992, 25, 7247. (16) Liang, G. L.; Noid, D. W.; Sumpter, B. G.; Wunderlich, B. Polymer, in press. (17) Liang, G.L. A Study of the Atomistic Details of Structure and Dynamics of Polymethylene Crystals via Molecular Dynamics Simulations. Ph.D. Dissertation, The University of Tennessee, Knoxville, Aug 1993.
