induced crystallization of single-chain polyethylene on a graphite surface: molecular dynamics...
TRANSCRIPT
PHYSICAL REVIEW E 84, 011803 (2011)
Induced crystallization of single-chain polyethylene on a graphite surface:Molecular dynamics simulation
Hua Yang (��),1,* Xiao Jun Zhao (���),1 and Miao Sun (��)2
1College of Chemistry, Tianjin Key Laboratory of Structure and Performance for Functional Molecule, Tianjin Normal University,Tianjin 300387, People’s Republic of China
2School of Chemical and Environmental Engineering, Harbin University of Science and Technology, Harbin 150080,People’s Republic of China
(Received 19 July 2010; revised manuscript received 26 January 2011; published 14 July 2011)
Molecular dynamics (MD) simulations have been carried out on the crystallization of single-chain polyethylene(PE) which was adsorbed on a graphite (001) surface on one side and exposed to vacuum on the other at differenttemperatures. The MD simulation data have been analyzed to provide information about the crystallizationprocess of polymer adsorbed on the solid substrate. The isothermal crystallization of PE proceeds in two steps:(1) adsorption and (2) orientation. The results detail the radial density distribution function, ordered parameters,local bond-orientational order parameters, and the local properties displayed in layers of the polymer parallel tothe graphite and vacuum interfaces. It was also shown that the film thickness affected the critical crystallizationtemperature of the adsorbed polymer on the substrate surface. Furthermore, the influence of the graphite surfacearea on the crystallization of PE is discussed by comparing the crystallinity evolution of PE on graphite withdifferent coverage.
DOI: 10.1103/PhysRevE.84.011803 PACS number(s): 36.20.−r, 83.10.Mj
I. INTRODUCTION
If a solid surface is exposed to a polymer solution, polymerscan be adsorbed onto the surface and form a thin or ultrathinfilm. This is important to many applications such as adhesives,coatings, lubricants, and composite materials [1]. The behaviorof polymers in ultrathin films draws considerable theoreti-cal and experimental attention because their structures andproperties are significantly different from those in thick filmsand bulk polymers [2–7]. The polymer-air or polymer-vacuumand polymer-solid interfaces are outside of the thin film. Themobility and behavior of polymer chain segments at each of theinterfaces is very different. Either the polymer-air or polymer-vacuum interface shows increased mobility compared to thepolymer-solid interface as the solid surface can retard polymerchain mobility. Polymer chains tend to orientate parallel toa solid surface. Crystallization is a typical case of polymer,which has long been investigated since the discovery of thechain-folded mode of crystallization [8,9]. The crystallizationof polymers in the presence of a solid surface may be differentfrom bulk polymer. Therefore more work should focus on thistopic.
Obtaining detailed information on the conformation anddynamics of polymers on a surface could greatly aid thedevelopment of new polymer materials. Many experimentsinvestigating polymer crystallization on atomically flat sur-faces, e.g., graphite, molybdenite (MoS2), KBr, and mica, haveshown that the solid surface influences the crystallization andthat the lamellae are much thicker than in the bulk. Traczand co-workers [10–15] observed the interface morphologyof polyethylene (PE) on graphite and MoS2 surfaces byatomic force microscopy (AFM) [10–13]. They suggested thatcrystallization of PE in contact with an atomically flat substrate
proceeds in two steps: adsorption and orientation. Wang et al.also studied the crystalline morphologies of poly(bisphenolA hexane ether) films using AFM [14]. They found thatthe film’s thickness had significant influence on the lamellarorientation at the surface. The concentration of the edge-onlamellae increased as the film thickness increased. Fourierinfrared spectroscopy was used to observe the conformationalordering and crystallization of polyethylene oxide (PEO) inthe presence of KBr surface by Geng and co-workers [15].They observed the crystallization process and showed thePEO chains adsorbed are more likely parallel to the surface ofKBr. Prokhorov and Nitta [16] also applied AFM to visualizethe crystalline conformations of PE on mica and graphiteat elevated temperatures. They showed that crystallizationquickly proceeds at cooling to room temperature due to theexpected rapidity of the intramolecular coil-to-crystal con-formational transition. However, detailed structural changesof polymers on solid surfaces are still difficult to graspexperimentally.
Computer simulations (especially MD) can provide es-sential information at the molecular level [8,17–19], whichis difficult to access using current experimental techniques.Monte Carlo (MC) and molecular dynamics simulations havebeen widely used to study the properties and behaviors ofpolymers, both in bulk and near surfaces. Previous simulationshave shown important information about polymer crystalliza-tion on a solid surface. Doye and Frenkel [20] studied thestructure and free energy landscape of a semiflexible latticepolymer in the presence of the surface of a polymer crystalby MC simulations. Guo et al. [21] explored the behaviorof a single long chain PE on a solid surface using MDsimulations. Mavrantzas and co-workers [22,23] showed thedetailed static properties and dynamics behavior of a densepolymer melt adsorbed on a solid surface on one side andexposed to vacuum on the other by the atomistic simulations.Ma et al. [24] simulated polymer crystallization confined
011803-11539-3755/2011/84(1)/011803(8) ©2011 American Physical Society
HUA YANG, XIAO JUN ZHAO, AND MIAO SUN PHYSICAL REVIEW E 84, 011803 (2011)
in rigid nanotube and in thin films. Kallrot et al. [25] alsostudied the dynamics of polymer adsorption from bulk solutiononto planar surface by Brownian dynamics simulations andMC simulations. MC and MD simulations were developedto study the structure and energetics of crystal nucleationphenomena in PE and low molecular weight n-alkane analogsby Rutledge’s group [26–28]. They characterized orientation-induced nucleation in PE and also observed the critical nucleusin oriented polymer melts. However, none of them studiedthe influences of temperature, chain length, and surface areaon the crystallization of polymer on a solid surface directly,which is important in the processing and application ofcrystalline polymer materials. In our previous MD simulationstudies, crystallization of single PE chain on nanotube hasbeen observed, and structure of final crystalline has beenanalyzed [29]. The nanotube surface is cylindrical, but graphiteprovides a flat surface. A distinct crystallization process maybe observed for PE on the graphite surface. Therefore, it isthe aim of our present work to explore the crystallization ofpolymers with different chain lengths on a solid surface atdifferent temperatures.
In this paper, we present the results of MD simulations fora polymer chain on a solid surface. In particular we attemptto establish the relation between crystallization temperatureand crystallinity. At the same time, we also wish to identifythe influence of chain length and relative surface area onthe structural and dynamic properties of polymers on asolid surface. Compared to complex polymer materials, linearalkanes provide well-defined model systems for studying thecomplex crystallization behavior of polymers in the bulk andnear surfaces [30]. Similar to Mavrantzas and co-workers[22,23], we have studied the crystallization of PE with differentchain lengths on a graphite surface at different temperatures.All of the investigations are mainly concerned with the effectof polymer-surface and polymer-polymer interactions (van derWaals interactions that chain atoms experience are due tointeraction with other chain atoms and the surface). Thus,reference to previous studies [20–24] shows that the solventeffect can be neglected. Our simulations would be a goodmodel for bad solvent conditions. Atomistic simulations canprovide insight into the microscopic processes involved inpolymer crystallization on a solid surface, and thus it is hopedour simulations will assess and refine the current theories andperhaps develop new theories.
II. MODELS AND SIMULATION METHODS
The physical system we studied in this paper is about asingle-chain PE adsorbed on graphite on one side and exposedto vacuum on the other. First, we built a single crystal cell ofgraphite with the cell parameters a = b = 2.46 A, c = 6.80A, α = β = 90◦, and γ = 120◦. Then the (001) surface wascleaved from the cell. In our simulations, the surfaces were20 × 20 (S1) and 40 × 40 (S4) supercells, with a thickness of∼12 A. The periodic boundaries were applied to the simulationbox. Parameter c was enlarged to 100 A to ensure that theinteractions between the adsorbed PE and the periodic imagesof graphite in the top plane could be ignored. In this waythe three-dimensional (3D) periodicity inherent in the modelwas transformed into actual two-dimensional (2D) periodicity
xy
z
FIG. 1. (Color online) The initial model of PE with 500 repeatedunits on the graphite (001) surface.
thus simulating an infinity extended surface. PE chains ofdifferent lengths (300, 500, 750, 1000 repeated units) were puton the graphite surface. The graphite surface was constrainedthroughout our simulations. As an example, the initial modelof PE with 500 repeated units on the surface (S1) is shown inFig. 1, which is denoted by PE500-S1.
Following previous studies [21–23,31–37], we treated CHx
groups as united atom to simplify the calculations. TheDreiding force field [38] has been successfully used in theinvestigations on the mechanism of polymer crystallization[32–36]. Thus, we choose the Dreiding force field for oursimulations. The CHx groups use the potential of the Dreidingforce field; the graphite carbon atoms adopt the same potentialas the aromatic carbon atom in the Dreiding force field. Thetotal potential energy (Etot), which includes bonding energy(Ebond) and nonbonding energy (Enonbond), can be expressed as
Etot = Ebond + Enonbond = Eb + Eθ + Eφ + EvdW, (1)
where Eb is the bond stretching energy, Eθ is the valenceangle bending energy, Eϕ is the dihedral torsion energy, andEvdW is the van der Waals interaction energy. The EvdW wascalculated with a cutoff of 9.5 A and a buffer length of 0.5 A.The functional form and parameters used in the force field arelisted in Ref. [38].
With the initial models built, energy minimizations wereperformed to relax the local unfavorable structure of thepolymer chain. Subsequently, we performed canonical MDsimulations with a temperature range of 300–700 K with 20-Kincrements. Simulations were also performed at temperaturesof 750 and 800 K. The total duration of the MD simulationwas 3000 ps for the PE300-S1, PE500-S1, PE750-S1, andPE500-S4 systems, and 5000 ps for the PE1000-S1 system.Every simulation was repeated three times to ensure thereproducibility of the results. The equations of motion wereintegrated with a time step of 0.001 ps. Simulation temper-atures were maintained using a Hoover thermostat [39,40],
011803-2
INDUCED CRYSTALLIZATION OF SINGLE-CHAIN . . . PHYSICAL REVIEW E 84, 011803 (2011)
TABLE I. Details of the PE-graphite models in this work.
Label Chain length, N Surface parameter Simulation time (ps)
PE300-S1 1 × (CH2CH2) 300 x = y = 49.2 A α = 120◦ 3000PE500-S1 1 × (CH2CH2) 500 x = y = 49.2 A α = 120◦ 3000PE750-S1 1 × (CH2CH2) 750 x = y = 49.2 A α = 120◦ 3000PE1000-S1 1 × (CH2CH2) 1000 x = y = 49.2 A α = 120◦ 5000PE500-S4 1 × (CH2CH2) 300 x = y = 98.2 A α = 120◦ 3000
with a relaxation time of 0.1 ps. A detailed description of allsimulated systems is given in Table I. All the simulations wereperformed using MATERIAL STUDIO software packages fromAccelrys, Inc.
III. RESULTS AND DISCUSSION
A. Process of isothermal crystallization of PE750-S1
MD simulations have provided insight into polymer crys-tallization. Our simulations investigate the adsorption andorientation processes of a PE chain on a graphite surface.Figure 2 shows the relaxation process of PE750 on graphite(S1) at 400 K. The PE chain is firstly adsorbed onto the graphitesurface gradually converting into an ordered four-layer lamel-lae. The PE chain adopts a preferred parallel orientationto the graphite plane in the layer-by-layer crystallization ofPE. The structural characteristics of the lamellae obtainedby our simulations are in agreement with the experimentalresults [12,16]. Figure 3 depicts an enlargement of the lastconformation of PE750-S1 at 400 K. We denote a direction onthe graphite surface (the arrow) in Fig. 3. The PE chain orientsalong the direction at a small angle. We find two main ordered
1ps 50ps 100ps 300ps
500ps 1000ps 2000ps
Top View
Side View
Top View
Side View
3000ps
FIG. 2. The isothermal relaxation process for PE750 on graphite(S1) at 400 K.
domains from the conformation of PE750-S1 at 3000 ps. Theordered orientations are the same for the PE chain in thesetwo domains relative to the graphite texture, which is shownin Fig. 3.
Radial density distribution function P (z) is defined as theprobability of finding CHx (x = 2,3) at a distance z from thegraphite surface. In order to fully describe the adsorptionprocess of PE on graphite, we calculated P (z) for PE750-S1with a time evolution of P (z) at 400 K [Figs. 4(a) and 4(b)].CHx has a wide distribution when the relaxation begins.However, as the simulation proceeds, the PE chain is adsorbedonto the graphite surface; four peaks appear at 3.5, 7.5, 12, and15 A. Early in the simulation time, the heights of all four peaksincrease quickly, corresponding to the adsorption process.They then fluctuate around particular values [the sequence ofthese values is P (3.5) > P (7.5) > P (12) > P (15)]. More PEsegments are adsorbed onto the PE layer near the surface. Thisdemonstrates a two-stepped isothermal crystallization process.
B. Structure of PE on a solid surface
In order to analyze the properties of PE adsorption andcrystallization upon a graphite surface, we must get to thebottom of the structure of PE. Figure 5 displays the orderedstructure of PE300, PE500, PE750, and PE1000 on graphite(S1) at 400 K after MD simulation. The local mass density[ρ(z)] was calculated at different distances (z) for the lastconformations of PE with different chain lengths on graphite(S1) at 400 K and shown in Fig. 6. The four PE chainscrystallize on the same graphite surface. The number of layersdecreases as the PE chain shortens. Two, three, four, andsix layers form with PE300-S1, PE500-S1, PE750-S1, andPE1000-S1, respectively. The height of the peak decreases
FIG. 3. (Color online) An enlarged part of the last conformation(3000 ps) of PE750-S1 at 400 K.
011803-3
HUA YANG, XIAO JUN ZHAO, AND MIAO SUN PHYSICAL REVIEW E 84, 011803 (2011)
FIG. 4. (Color online) (a) Time evolution of radial densitydistribution function P (z) for PE750-S1 at 400 K (time axis is notlinear). (b) P (3.5), P (7.5), P (12), and P (15) for PE750-S1 as afunction of simulation time.
with increasing z. This may result in a decrease in the attractiveinteraction between graphite and CHx of these layers.
Comparisons of the local mass density distribution of thefour systems show that the peaks in each system are locatedat approximately the same distance; this also corresponds to
PE300 PE500 PE750 PE1000
FIG. 5. Ordered structure of PE300, PE500, and PE750 ongraphite (S1) at 400 K after 3000-ps MD simulation, and orderedstructure of PE1000 on graphite (S1) at 400K after 5000-ps MDsimulation.
0 5 10 15 20 25 30
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
r(z
) g/
cm
3
PE300 PE500 PE750 PE1000
z ( A )O
FIG. 6. (Color online) Local mass density distribution for the lastconformations of PE300, PE500, PE750, and PE1000 on graphite(S1) at 400 K. The vertical dashed lines are used to define the bordersof the six regions.
the different layers. Six peaks appear in PE1000-S1, whichis the longest PE chain measured. The peaks are measured at3.5, 7.5, 12, 15, 19, and 22.5 A. In contrast, there are onlythree peaks produced by the PE melt adsorbed on graphite[22,23]. The simulations show more peaks present for PE750and PE1000 crystal on graphite (S1). PE crystal on graphiteis an ordered layerlike structure. According to the localmass density distribution profile of the layered structure, theinterfacial area can be divided into six distinct regions. The sixregions are depicted in Fig. 6 by vertical dashed lines and willbe helpful in our calculation of the crystallinity of PE.
C. Crystallization of PE on graphite at different temperatures
The degree of crystallinity is a simple and importantparameter. It measures the amount of material contained withinthe ordered region and amorphous region [41]. Recently, analternative method (site ordered parameter) [36,42] has beenused to calculate the crystallinity of a polymer. This methodis based on the assumption that a given site in the systemcan be endowed with a site order parameter which resultsfrom the order described by several vectors. We first dividedthe simulation box into many domains by planes parallel tothe xy, xz, and yz planes. For one site, the two side lengths(x and y directions) are 9.84 A, and the height length is equalto the layer’s height. This means that the domains belongingto different layers possess different height lengths. Then, wecalculated the site ordered parameter [ASOP(k)] of the kth site,which is defined by
ASOP(k) = 32 〈(⇀
ei · ⇀
ej )2〉R − 12 , (2)
where k denotes the kth domain,⇀
ei and⇀
ej are two differentsubbond vectors (which are formed by connecting the centersof two adjacent bonds) within the domain, the smallest domainR approximately equal to the work of Yu et al. [42]. Oursimulation box contains 150 domains. If the calculated ASOP(k)is higher than a critical value (∼0.7), we consider that the kthsite is an ordered domain. The number of the ordered domains
011803-4
INDUCED CRYSTALLIZATION OF SINGLE-CHAIN . . . PHYSICAL REVIEW E 84, 011803 (2011)
300 400 500 600 700 8000.000.050.100.150.200.250.300.350.400.450.500.550.600.65
Ave
rage
Cry
stal
linity
Temperature (K)
PE300-S1 PE500-S1 PE750-S1 PE1000-S1
FIG. 7. (Color online) Average crystallinity evolutions of PE300-S1, PE500-S1, PE750-S1, and PE1000-S1 with increasing temper-ature. The error bars are the standard deviation calculated from thetime average.
is denoted as Nc. It is convenient to calculate the crystallinityχ of a polymer model by the ratio
χ = Nc
N, (3)
where N is the number of domains containing the PE chain.Most of the domains contain several extended PE chains.
There may be no segments, only one loop or tail of PE chainat the polymer-vacuum interface in some domains. If one sitecontains only an extended PE chain, there will be about six orseven subbond vectors in the site. The ASOP(k) of the site maybe larger than 0.7. This makes an incorrect description of thesites of the structure. In order to avoid the misinterpretationof the sites at the polymer-vacuum interface, ASOP(k) of suchsites are therefore set to zero.
By using the definition of crystallinity, we analyzed theinfluence of temperature on the crystallization process ofdifferent PE chains on the graphite surface. The crystallinityof the four systems are calculated by averaging χ from 2501to 3000 ps (from 4501 to 5000 ps for PE1000) at eachsimulation temperature. Figure 7 displays the changes ofaverage crystallinity (χavg) for PE300-S1, PE500-S1, PE750-S1, and PE1000-S1 with increasing temperature. The χavg ofthe four systems fluctuate around different values at lowertemperatures, and decrease quickly at high temperature. Theχavg of PE300-S1 is the highest of the four systems regardlessof changes in temperature. This is because in an orderedstructure the short chain PE can change more easily than thelong chain, which forms a thick film on the same graphitesurface. Daoulas et al. [22,23] showed that three adsorbedlayers lie between graphite and PE bulk in the PE film. The lastconformations of PE300-S1 and PE500-S1 are two layers andthree layers, respectively, implying that they are affected bythe surface. PE750-S1 and PE1000-S1 form four-layered andsix-layered structures, respectively. Their properties may bemuch more similar to the bulk. Thus the χavg of PE300-S1 andPE500-S1 are different from those of PE750-S1 and PE1000-S1. Additionally the χavg of PE750-S1 and PE1000-S1
300 400 500 600 700 800 900 1000660
680
700
720
740
760
780
800
820
Crit
ical
cry
stal
lizat
ion
tem
pera
ture
(K
)
Chain length
FIG. 8. Critical crystallization temperature changes as a functionof chain length.
are difficult to distinguish at lower temperatures before theydecrease at high temperatures.
If we define that the critical crystallization temperatureis the temperature when χavg of polymer is lower thanthe critical value (0.3), the sequence of the four systems’critical crystallization temperature is TPE300-S1 > TPE500-S1 >
TPE750-S1 > TPE1000-S1. The critical crystallization temperaturedecreases with increasing chain length, which is shown inFig. 8. The long PE chain produces broader distribution fromthe graphite surface compared to the narrow distribution of theshort chain. This corresponds to an increase in their thicknesswith increasing PE chain length. This result suggests there isa thickness effect on the critical crystallization temperatureof adsorbed polymer on the surface. Critical crystallizationtemperatures of the four systems decrease with increasingthickness of PE film. PE chain near the graphite surface can beinduced to a particular orientation. Their critical crystallizationtemperatures are all higher than the PE’s [33]. This is incontrast with our previous work which investigated PE/C60nanocomposites. The reason could be that the large curvaturesurface of C60 does not fit the straight PE chain; but graphitehas a flat surface, which can induce crystallization for PE.Like the experimental results [43,44], the ordered layersadsorbed on the graphite surface could be observed at highertemperatures than that of bulk polymer.
Figure 9 shows the time evolution of crystallinity forsingle-chain PE with different chain lengths at 400 K. Initiallythe crystallinity of each chain length increases quickly in theearly stage and then slows down thereafter. If we define thatthe crystallization time is the time when χavg of the polymerreaches the critical value (0.3), the PE300-S1 is the first withPE1000-S1 taking the longest. The inset in Fig. 9 is the plotof crystallization time versus chain length. Crystallizationtime increases with increasing chain length which meansPE1000-S1 needs much more time to crystallize than the othersystems. Our investigations have shown that the long PE chainforms a thick film at the graphite surface (S1), indicating thatthe thick polymer film needs more time to crystallize.
The time evolutions of crystallinity for PE1000-S1 atseveral temperatures are displayed in Fig. 10. At 400 and
011803-5
HUA YANG, XIAO JUN ZHAO, AND MIAO SUN PHYSICAL REVIEW E 84, 011803 (2011)
10 100 1000-0.1
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
300 400 500 600 700 800 900 10000
100
200
300
400
500
600
700
800C
ryst
alliz
atn
ime
(ps)
Chain length
Cry
stal
linity
Time (ps)
PE300 PE500 PE750 PE1000
FIG. 9. (Color online) Time evolutions of crystallinity withdifferent chain lengths PE on graphite surface (S1) at 400 K. Theinset plots the crystallization time of different chain length PE ongraphite surface.
500 K the crystallinity increases quickly from 0 to 1500 psand thereafter fluctuates around particular values. At 600 Kthe crystallinity increases a little more slowly, but at 700 Kthe crystallinity fluctuates around a low value throughout thesimulation. This is similar to our previous study on PE/C60nanocomposites [33]. The nucleation and crystal growthcan cause an increase in crystallinity of the polymer. Lowtemperatures favor the nucleation process, thus, the currentresults also show that nucleation and crystal growth controlthe initial stage and rearrangement after that, respectively.
D. Local properties in the layers parallel to the graphiteand vacuum interfaces
In order to show more details of the isothermal crystalliza-tion process, we try to calculate the properties of the different
0 1000 2000 3000 4000 50000.0
0.1
0.2
0.3
0.4
0.5
Cry
stal
linity
Time (ps)
400K 500K 600K 700K
400K 500K
600K
700K
FIG. 10. (Color online) Crystallinity evolutions of PE1000-S1 at400, 500, 600, and 700 K.
10 100 1000
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
A
Time (ps)
layer1 layer2 layer3 layer4 layer5 layer6
layer2layer1
layer4layer3
layer6layer5
FIG. 11. (Color online) The time evolution of ordered parameterA of the six layers for PE1000-S1 at 400 K.
layers. The ordered parameter Ai of the ith layer is calculatedby averaging ASOP of the Ni sites in the ith layer:
Ai = 1
Ni
Ni∑ki=1
ASOP(ki). (4)
The time evolution of ordered parameter A of the six layersfor PE1000-S1 at 400 K is displayed in Fig. 11. A1 quicklyincreases from 0.0 to 0.58 and then fluctuates around 0.58. TheA values of the other five layers all increase before 1500 psand then fluctuate around their equilibrium value, respectively.The sequence of A is A6 > A1 > A2 ≈ A5 > A4 > A3 at theend. Layer 1 is nearest to the surface; the graphite surfaceinduces the orientation of the PE chain in layer 1 accordingto its texture (see Fig. 3). The interaction between PE chainsegments in layer 1 and the surface is the strongest interaction.Therefore PE chain segments have limited mobility in layer 1.The number of CHx and the ordered parameter of layer 1 andA1 show very little change after reaching their equilibriumvalue. On the contrary, PE chain segments in layer 6 can movefreely, and more local ordered domains form. A6 takes thebiggest equilibrium value. To conclude, the graphite affectsthe orientation of the first adsorption PE layer the most. Thisresult is consistent with the results of Harmandaris [23], whichstate that the influence of the graphite on the conformationalrelaxation of the adsorbed PE is limited to the first layer.
In order to show the local bond-orientational order of PEalong the z axis, we calculated and showed the local bond-orientational order parameter SB(z) for the last configurations(5000 ps) of PE1000-S1 simulated at 400, 500, 600K, 700,and 800 K in Fig. 12. SB(z) is defined by
SB(z) =⟨
3 cos2(φ(z)) − 1
2
⟩bond
, (5)
where ϕ(z) is the angle between the subbond vector and zaxis, and 〈· · · 〉bond denotes the average over the subbonds ina slab between z and z + dz. We set dz = 0.5 A during thecalculations of SB(z). The parameter SB(z) would assume avalue of 1.0, 0.0, or –0.5, respectively, for subbonds in a slab[z, z + dz] perfectively parallel, random, or perpendicular to the
011803-6
INDUCED CRYSTALLIZATION OF SINGLE-CHAIN . . . PHYSICAL REVIEW E 84, 011803 (2011)
0 10 20 30-0.5-0.4-0.3-0.2-0.10.00.10.20.30.4
Z (angstrom)
-0.6-0.4-0.20.00.20.4
SB(z
) 400K
SB(z
)
-0.6-0.5-0.4-0.3-0.2-0.10.00.10.20.3
SB(z
)
-0.6-0.4-0.20.00.20.4
SB(z
)
-0.5-0.4-0.3-0.2-0.10.00.10.20.3
500K
600K
700K
SB(z
)
800K
FIG. 12. The local bond-orientational order parameter SB (z) forthe last configurations of PE1000-S1 simulated at 400, 500, 600, 700,and 800 K.
z axis. Figure 12 shows that there are some orientational layers,where SB(z) reaches –0.45, for PE on the graphite surface.The PE chain is almost perpendicular to the z axis in theselayers. In the case of 400 K, we can see five local orientationallayers. The layers near the vacuum are more complicated thanthose near the graphite surface. SB(z) decreases graduallyin the orientational layers near the vacuum with increasingtemperature. These layers disappear at temperatures of 700and 800 K, resulting in only three orientational layers near thegraphite surface. This implies that the graphite only affectsthe local orientation of the first three adsorbed layers. This isdifferent to the effect of graphite on the ordered parameter ofdifferent layers, which is mainly limited to the first adsorptionlayer. These three layers correspond to the three adsorptionlayers for PE on a graphite surface [22,23].
E. Crystallization of PE on graphite with different surface area
The graphite surface area may affect the crystallization ofPE on graphite. We compared the crystallization process ofPE500-S1, PE500-S4, and PE300-S1 at 400 K and show thecrystallinity evolutions of the three systems in Fig. 13. Thecrystallinity of all three systems increases quickly and even-tually fluctuates around aparticular value. PE500-S4 forms asingle layer ordered structure with unsaturated coverage. Theconformation of adsorbed chain gets kinetically arrested andthen can do only limited local reorientation. The energeticallymore favorable configuration is when the whole chain is plas-tered on the graphite surface in a single layer instead of making
10 100 1000-0.1
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Cry
stal
linity
Time (ps )
PE500-S1 PE500-S4 PE300-S1
PE500-S4
PE500-S1
PE300-S1
FIG. 13. (Color online) Crystallinity evolutions of PE300-S1,PE500-S1, and PE500-S4 at 400 K.
multilayers. The probability that PE chain segments adsorb andinduce crystallization on a graphite surface is high. PE300-S1and PE500-S1 form two- and three-layer ordered structureswith saturated coverage, respectively. The probability thatPE chain segments adsorb and induce crystallization on thegraphite surface must decrease. Thus PE500-S4 is the firstone to reach its equilibrium value and its crystallinity is thebiggest. Crystallinity of PE300-S1 is a little bigger than that ofPE500-S1. The large graphite surface favors PE crystallization.The probability (P) of various PE chains to adsorb along thesame graphite surface (S1) at 400 K is shown in Fig. 14. Itis obvious that PE300 is easily adsorbed and oriented on thegraphite directly. On the same graphite surface (S1), long PEchain forms thick film. PE chain segments need more time tomove to the graphite surface. Thus P of the long chain must bebigger than P of the short chain. Combining with the resultsof Fig. 7, we may conclude that PE is easy to crystallize ongraphite with small coverage or a thin film on graphite.
300 400 500 600 700 800 900 1000
0.2
0.4
0.6
P
Chain length
FIG. 14. The probability (P) of various PE chains adsorbing alongthe same graphite surface (S1) at 400 K. P is calculated by averagingfrom 2501 to 3000 ps for PE-300-S1, PE500-S1, and PE750-S1 andfrom 4501 to 5000 ps for PE1000-S1.
011803-7
HUA YANG, XIAO JUN ZHAO, AND MIAO SUN PHYSICAL REVIEW E 84, 011803 (2011)
IV. CONCLUSION
We have presented results from MD simulations of thecrystallization process of a single PE chain adsorbed ona graphite surface at different temperatures. The isother-mal crystallization process goes through two stages, theadsorption and the orientation. The simulation systems aredivided into many layers parallel to the graphite surfaceaccording to their local mass density distribution function.There is a critical temperature for PE crystallization on agraphite surface. Our simulations have shown that thick PEfilm leads to low critical temperature. However, the criticalcrystallization temperature for PE on graphite is higher thanPE or PE-C60 composite. The graphite only affects the localorientation of the first three adsorbed PE layers, whereasits influence on the ordered parameter of adsorbed PE on
graphite is limited to the first layer. Therefore, PE is easyto crystallize on graphite that has small coverage or a thinfilm.
ACKNOWLEDGMENTS
This work is supported by the National Natural Sci-ence Foundation of China (Grants No. 20803052 and No.20871092), the Foundation of Tianjin Educational Committee(Grant No. 20070605), and the Foundation for the Teacherby the Tianjin Normal University (Grant No. 5RL065). Wealso thank Zhongyuan Lu for supplying the computationalresource and simulation software in Jilin University and NishaKanwar (University of Edinburgh) for help polishing theEnglish.
[1] R. A. L. Jones and R. W. Richards, Polymers at Surfaces andInterfaces (Cambridge University Press, Cambridge, 1999).
[2] I. C. Sanchez, Physics of Polymer Surfaces and Interfaces(Butterworth-Heinemann, Boston, 1992).
[3] X. Zheng, M. H. Rafailovich, J. Sokolov, Y. Strzhemechny,S. A. Schwarz, B. B. Sauer, and M. Rubbinstein, Phys. Rev.Lett. 79, 241 (1997).
[4] R. L. Jones, S. K. Kumar, D. L. Ho, R. M. Briber, and T. P.Russell, Nature (London) 400, 146 (1999).
[5] E. K. Lin, R. Kolb, S. K. Satija, and W. L. Wu, Macromolecules32, 3753 (1999).
[6] S. Granick, S. K. Kumar, E. J. Amis, M. Antonietti, A. C. Balazs,A. K. Chakraborty, G. S. Grest, C. Hawker, P. Janmey, E. J.Kramer, R. Nuzzo, T. P. Russell, and C. R. Safinya, J. Polym.Sci., Part B: Polym. Phys. 41, 2755 (2003).
[7] C. K. Ober, S. Z. D. Cheng, P. T. Hammond, M. Muthukumar,E. Reichmanis, K. L. Wooley, and T. P. Lodge, Macromolecules42, 465 (2009).
[8] T. Yamamoto, Polymer 50, 1975 (2009).[9] L. Mandelkem, Crystallization of Polymers (McGraw Hill,
New York, 1964).[10] A. Tracz, J. Jeszka, I. Kucinska, J. P. Chapel, and G. Boiteux,
Macromol. Symp. 169, 129 (2001).[11] A. Tracz, J. K. Jeszka, I. Kucinska, J. P. Chapel, G. Boiteux, and
M. Kryszewski, J. Appl. Polym. Sci. 86, 1329 (2002).[12] A. Tracz, I. Kucinska, and J. K. Jeszka, Macromolecules 36,
10130 (2003).[13] Y. Takenaka, H. Miyaji, A. Hoshino, A. Tracz, J. K. Jeszka, and
I. Kucinska, Macromolecules 37, 9667 (2004).[14] Y. Wang, C. M. Chan, K. M. Ng, and L. Li, Macromolecules 41,
2548 (2008).[15] Y. Geng, G. L. Wang, Y. H. Cong, L. G. Bai, L. B. Li, and C. L.
Yang, J. Polym. Sci., Part B: Polym. Phys. 48, 106 (2010).[16] V. V. Prokhorov and K. Nitta, J. Polym. Sci., Part B: Polym.
Phys. 48, 766 (2010).[17] K. Binder, Monte Carlo and Molecular Dynamics Simulations
in Polymer Science (Oxford University Press, New York, 1995).[18] P. Welch and M. Muthukumar, Phys. Rev. Lett. 87, 218302
(2001).[19] M. Muthukumar, Adv. Polym. Sci. 191, 241 (2005).[20] J. P. K. Doye and D. Frenkel, J. Chem. Phys. 109, 10033 (1998).
[21] H. X. Guo, X. Z. Yang, and T. Li, Phys. Rev. E 61, 4185 (2000).[22] K. C. Daoulas, V. A. Harmandaris, and V. G. Mavrantzas,
Macromolecules 38, 5780 (2005).[23] V. A. Harmandaris, K. C. Daoulas, and V. G. Mavrantzas,
Macromolecules 38, 5795 (2005).[24] Y. Ma, W. B. Hu, J. Hobbs, and G. Reiter, Soft Matter 4, 540
(2008).[25] N. Kallrot, M. Dahlqvist, and P. Linse, Macromolecules 42, 3641
(2009).[26] M. S. Lavine, N. Waheed, and G. C. Rutledge, Polymer 44, 1771
(2003).[27] N. Waheed, M. J. Ko, and G. C. Rutledge, Progress in
Understanding of Polymer Crystallization (Springer, Berlin,Heidelberg, 2007).
[28] P. Yi and G. C. Rutledge, J. Chem. Phys. 131, 134902 (2009).[29] H. Yang, Y. Chen, Y. Liu, W. S. Cai, and Z. S. Li, J. Chem. Phys.
127, 094902 (2007).[30] B. Q. Xie, G. M. Liu, S. C. Jiang, Y. Zhao, and D. J. Wang, J.
Phys. Chem. B 112, 13310 (2008).[31] M. Putz, J. Curro, and G. S. Grest, J. Chem. Phys. 114, 2847
(2001).[32] T. A. Kavassalis and P. R. Sundararajan, Macromolecules 26,
4144 (1993).[33] P. R. Sundararajan and T. A. Kavassalis, J. Chem. Soc. Faraday
Trans. 91, 2541 (1995).[34] S. Fujiwara and T. Sato, J. Chem. Phys. 114, 6455 (2001).[35] X. B. Zhang, Z. S. Li, H. Yang, and C. C. Sun, Macromolecules
37, 7393 (2004).[36] H. Yang, X. J. Zhao, Z. Y. Lu, and F. D. Yan, J. Chem. Phys.
131, 234906 (2009).[37] R. H. Gee, N. Lacevic, and L. E. Fried, Nat. Mater. 5, 39 (2006).[38] S. L. Mayo, B. D. Olafson, and W. A. Goddard, III, J. Phys.
Chem. 94, 8897 (1990).[39] S. Nose, J. Chem. Phys. 81, 511 (1984).[40] W. G. Hoover, Phys. Rev. A 31, 1695 (1985).[41] D. I. Brower, An Introduction to Polymer Physics (Cambridge
University Press, Singapore, 2002).[42] X. Yu, B. Kong, and X. Z. Yang, Macromolecules 41, 6733
(2008).[43] S. N. Magonov and N. A. Yerina, Langmuir 19, 500 (2003).[44] A. Tracz and G. Ungar, Macromolecules 38, 4962 (2005).
011803-8