DFT and MM calculation: the performance mechanism of pour point

depressants study

Jinli Zhanga,*, Chuanjie Wua,b, Wei Lia, Yiping Wanga, Hui Caoc

aSchool of Chemical Engineering and Technology, Tianjin University, 300072 Tianjin, ChinabCollege of Pharmaceuticals and Biotechnology, Tianjin University, 300072 Tianjin, China

cRefinery of Beijing Yanshan Petrochemical Corporation, 102503 Beijing, China

Received 13 March 2003; accepted 4 August 2003; available online 19 September 2003

Abstract

Adding pour point depressants (PPDs) to lower the cold filter plugging point (CFPP) of oils has been widely used as the most valuable way

in the world. To develop the new type of PPDs according to the oils of different kinds, many researchers have tried to study the performance

mechanism of PPDs with different methods. In this article, we have carried out this study with density function theory and molecular

mechanics calculation methods. From the results of different systems, we have found that: (1) Alkane molecule is non-polar but the methyl

groups on the chain ends have higher electronegativity than all the methylene groups. (2) The EVA (copolymer of ethylene and vinyl acetate)

molecule is divided into segments by the polar groups, and the segments are composed of carbon chains, while at the joint points of the

segments are ester groups. Calculation results show that the non-polar parts of EVA molecule have good affinity to the adjacent alkane

molecules. The rigidity of the carbon bonds neighboring to ester groups is enhanced by the introduction of ester groups, which can also help

the next segments to get into the next crystal units and accelerate the growth rate of the planes perpendicular to (001) plane. (3) The alkane

molecules absorbed on the PPD molecules can be bent, and the bending conformation brings steric hindrance effect to the molecules to

deposit on the surface near the PPD molecules. The relatively higher electronegativity of the methyl groups, which are bent out of the crystal

units, can also bring more repulsion effect to the alkane molecules to deposit. This helps to restrict the high growing velocity of (001) plane

and results in the uniformity growing rate in three dimensions. (4) If we want to get the good performance properties of PPDs, the carbon

number should be a little lower than the mean carbon number of the wax crystals. Then the acetate percent of EVA molecules should be

around 30% and the concrete value should be determined according to the oils used.

q 2004 Elsevier Ltd. All rights reserved.

Keywords: Pour point depressant; Mechanism; Density function theory; Molecular mechanics

1. Introduction

Adding pour point depressants (PPDs) to lower the cold

filter plugging point is one of the most important methods

for improving the low temperature flow properties of diesel

oils. Certain PPDs are known to have a significant effect on

both the rate of wax deposition and the resulting crystal-

lization [1–7].

A number of PPDs have been developed to affect the

kinetics of paraffin crystallization [8–10], however, it is

also found that all the PPDs have a lot of limitations to

perform well in different diesel oils. Many researchers have

tried to find a universal mechanism to explain the change of

the wax crystals in habit and particle size, from which the

product design of PPDs according to different kinds of

diesel oils would benefit. Now adsorption, co-crystal-

lization, nucleation, and improved wax solubility have

been accepted as the most widely used theories in

explaining the mechanism [11]. In the study processes,

many experimental and theoretical methods such as

thermodynamics theory, polymer physics theory, crystal-

lography theory, etc. have been used by different research-

ers. So far, many processes are in macroscopic view and do

not offer satisfactory results for the industrial applications. It

has generally been found that the molecules in such

complicated system are hard to ‘touch’ and research. It is

the hope of researchers to ‘observe’ how the PPD molecules

0016-2361/$ - see front matter q 2004 Elsevier Ltd. All rights reserved.

doi:10.1016/j.fuel.2003.08.010

Fuel 83 (2004) 315–326

www.fuelfirst.com

* Corresponding author. Tel.: þ86-22-27890044.

E-mail addresses: xinxing@tju.edu.cn (J. Zhang), wu_chuanjie@

yahoo.com.cn (C. Wu).

deposit on the wax crystal surface and then modify its

surface properties and orientation.

With the fast development of computational chemistry

these years, many scientists have used it as a powerful

tool to study their objects in molecular view, which can

present clear image of many chemical processes.

Quantum mechanics (QM), quantum chemistry, density

function theory (DFT), semi-empirical methods, and

molecular mechanics (MM) have been widely used for

calculating the static properties of the molecules and

molecular systems. Moreover, molecular dynamics (MD)

and Monte Carlo (MC) have been introduced to

calculate the dynamics and statistics properties of

molecular systems like nano-materials and life science

systems. Computational chemistry methods to reveal the

essence of some processes and phenomena have

been turned out to be a practicable way and a popular

trend to use.

Researchers studying the performance mechanism of

PPDs have also found some powerful tools from

computational chemistry, which would help them to

conduct research in new fields. Duffy and Rodger have

carried out much effective work these years in the field

of the mechanism study with computational chemistry

methods. They have completed the calculation on the

properties of molecules in a liquid heptane film on an

octacosane crystal surface with the MD program

DL_POLY [12], which uses standard MD techniques to

calculate the properties of solids and liquids. The comb-

shaped poly(octadecyl acrylate) molecule was selected as

the additive, which had much long side chains. With the

analysis of the results, it was found that the polymer

mixed well with the heptane to produce an additional,

strongly ordered layer that would provide a kinetic

barrier to any subsequent wax deposition [13,14]. Their

series results have given some useful concept of the

performance mechanism of the additives with long side

chains, but little have been done to the mechanism of

PPDs of other types in their study. There was no

information on the molecular design of PPDs, which

would bring direct benefit to the industry.

In our research, we have studied the mechanism of

PPDs with DFT and MM in vacuo to study the

interaction between normal alkane molecules and PPDs.

C20H42 was selected as the wax molecules, which will be

more close to the mean carbon number of wax crystal

molecules in diesel oils. Ethyl vinyl acetate (EVA) with

molecule weight of 2000 and 25% of acetate was

selected as the PPD. EVA is more widely used as diesel

oil additive in the world and has quite different structural

character with poly(octadecyl acrylate). Heptane is also

used as the solvent in the calculation.

All the calculation was carried out on LEGEND personal

computer (LEGEND Co.) with CPU P4 1.6G, hard disk 40G

and internal memory of 1.0G.

2. Calculation details

Considering the relatively high molecular weight and

linear structure of EVA molecules, we selected DFT and

MM as the calculation methods for investigating the static

properties, and MD in vacuo was selected as the dynamics

and conformation study method.

2.1. Density function theory calculation method

DFT has turned out to be an efficient and widely used

way of quantum chemistry in calculating the static proper-

ties of different molecules, especially large molecules.

Theoretically DFT is based on the conclusion that the

energy of the multi-electron system ðEÞ is the function of the

single variable of electron density ðrÞ [15]:

EðrÞ ¼ TðrÞ þ JðrÞ þ VxcðrÞ ð1Þ

E ¼ð1

{T½rðrÞ� þ J½rðrÞ� þ Vxc½rðrÞ�}·rðrÞdr ð2Þ

Where T ; J and Vxc are kinetic energy, coulomb energy and

exchange–correlation energy, respectively; rðrÞ is the

electron density function; and r is the radius of atoms.

The basic calculation equation of DFT is the Kohn–

Sham self-consistent equation:

{h½rðrÞ� þ j½rðrÞ� þ vxc½rðrÞ�}wðrÞ ¼ 1·wðrÞ ð3Þ

where h; j; vxc are the Hermitian operators of kinetic energy,

coulomb energy, and exchange–correlation energy, respect-

ively; wðrÞ is the eigenfunction of the operators, while 1 is

their eigenvalue.

To solve Eq. (3) and find the solution of the electron

density rðrÞ according to the minimum energy, we can

calculate many other static properties with minor errors,

such as the equilibrium structures of molecules; transition

states and reaction paths; molecular properties like elec-

trical, magnetic, optical, etc. spectroscopy from NMR to X-

ray; reaction mechanisms in chemistry and biochemistry;

intermolecular interactions giving potentials which may be

used to study macromolecules, solvent effects, crystal

packing, etc.

In our research, DFT has been used to calculate the

equilibrium conformation, electrical properties, dipole, and

solvent effect (only EVA) of normal alkane, vinyl acetate

and simple co-polymer EVA in heptane. All the calculation

level is B3LYP/6-31G(d, p). Here B3LYP (Becke’s three

parameter hybrid functional using the correlation functional

of Lee, Yang, and Parr, which includes both local and non-

local terms correlation functional) is a widely used DFT

method [16]. And 6-31G(d,p) [17–21] is the selected basis

set for studies.

Heptane was used as the solvent and solvent effect was

calculated. Polarized continuum Model (PCM) was selected

to describe the self-consistent reaction field (SCRF) of the

solution and the dielectric constant of heptane was 1.92.

J. Zhang et al. / Fuel 83 (2004) 315–326316

2.2. Molecular mechanics calculation method

MM calculation is a widely used method in the polymer

chemistry study. In this method, particles are taken as the

classic ones and Newtonian mechanics principles can be

applied to solve their movement equations. Vibration,

rotation, and translation movement of the particles are all

neglected in this method.

In our MM calculation, Amber force field [22] was

applied to different systems.

2.3. Molecular dynamics simulation method

MD was used as the conformation selecting tools. In

MD simulation, atoms’ movement was simulated

with classical mechanics and the force exerted on the

atoms is given by force field functions. In MD

simulation, Amber force field [22] was used. The other

parameters used in the simulation are listed in Table 1.

Simulated annealing was also used to give a relatively

stable conformation that is nearest to have global

minimum conformation energy under the simulation

temperature.

Since in the MD simulation it is easy for molecules to

overcome the local minimum conformation energy and

most of the probable conformation will be displayed in

the simulation process until a relatively stable confor-

mation after annealing, it is a good way to study the

changing rules of the bonds formed with different atoms

and select the annealed conformation to explain the rules.

However, we know that the conformation change is quite

complicated for EVA molecules with a long chain, both

in vacuum or in the real diesel fuels, then in the

following parts of this article, the conformation from MD

simulation was called as ‘a MD random conformation’,

thought it has been annealed under the simulation

temperature.

3. Results and discussions

3.1. DFT calculation

3.1.1. Atom charges distribution of a normal alkane

molecule

Wax crystals are the mixture of the normal alkane

molecules with relatively high molecular weight. We have

found one n-alkane molecule C20H42 with three dimension

structure as initial conformation from the website NIST

chemistry Webbook [23]. This result can give enough

information of the main charge characters of the n-alkane

molecules of all kinds considered, though there will be a lot

of other conformations of n-alkane molecules in the solution

or in the crystals. In addition, the calculation was performed

in vacuum.

The calculated conformation of the alkane molecule

is shown in Fig. 1, and the atom charges are listed in Tables 2

and 3.

The optimized energy of the molecule is 2787.533 a.u.

(atomic unit) on the calculating level, and the dipole is

0.0534 Debye.

From the results, several points can be summed up as

following:

(1) The optimized conformation of this molecule is a helix

structure, which has a relatively high stability.

Certainly this is not the only conformation in the

systems.

(2) The molecule has a little dipole, which may be induced

by the asymmetry caused by helix or torsion of the

whole molecule, however, it is determined that this is a

non-polar or little polar molecule.

(3) The carbon atoms at the end, i.e. C (19) and C (20),

which are surrounded by three atoms, have signifi-

cantly higher electronegativity than the other atoms in

this molecule. On the other hand, the neighbor

hydrogen atoms of these two kinds of carbon atoms

have higher electropositivity than other hydrogen

Table 1

Parameters used in molecular dynamics simulation

Items Values

Ensemble Canonical ensemble NVT

Thermostat Nose-Hoover

Relaxation time 0.1 ps

Heat time 10 ps

Run time 5 ps

Cool time 10 ps

Dynamics time step 0.001 ps

Starting temperature 2 K

Simulation temperature 300 K

Final temperature 298 K

Dynamics temperature step 1 KFig. 1. Atom labels and the DFT optimized structure of C20H42 molecule.

J. Zhang et al. / Fuel 83 (2004) 315–326 317

atoms. The carbon atoms neighboring to the end carbon

atoms, i.e. C (17) and C (18), have relatively lower

electronegativity because of displacement of the

covalence electron cloud and the torsion of the bond

angles.

(4) When the hydrogen atoms’ charge was summed into

the heavy atoms (atoms except hydrogen atoms), the

charge turned out to be the function groups’. From the

charges with hydrogen calculated in, we also find that

the methyl groups on the end has higher electronega-

tivity, while the methylene groups neighboring to them

has higher electropositivity than the other groups of

this molecule.

3.1.2. The molecular property of vinyl acetate

Vinyl acetate (VA) is one of the monomer of EVA,

which offers the acetate percent of the EVA molecules and

bring polar atoms to them. The optimized conformation of

this molecule is shown in Fig. 2. The calculated structure

parameters and atom charges are listed in Tables 4 and 5.

The optimized Becke3LYP conformation energy is

2306.459 a.u., and the dipole of this molecule is

3.837 Debye.

From the results, several points can be summed up:

(1) This molecule has some polarity, but for the coex-

istence of the double bonds of –CyO and –CyC. The

asymmetry has been improved and the polarity is not

quite strong.

(2) O (1) and O (5) have performed very high electro-

negativity, while C (2) between them have shown a

strong electropositivity owing to polar covalence

caused by solely the oxygen atoms.

Table 2

Atom charges of C20H42

Label Atom Charges

1 C 20.175403

2 C 20.173994

3 C 20.171340

4 C 20.173799

5 C 20.177508

6 C 20.171415

7 C 20.177385

8 C 20.177351

9 C 20.171259

10 C 20.177215

11 C 20.174549

12 C 20.171623

13 C 20.174501

14 C 20.173811

15 C 20.165346

16 C 20.166076

17 C 20.173408

18 C 20.173414

19 C 20.317455

20 C 20.317322

21 H 0.086960

22 H 0.086927

23 H 0.087375

24 H 0.086911

25 H 0.086119

26 H 0.091598

27 H 0.087404

28 H 0.086869

29 H 0.085276

30 H 0.086307

31 H 0.091316

32 H 0.086277

33 H 0.086369

34 H 0.085263

35 H 0.086157

36 H 0.085315

37 H 0.086157

38 H 0.091598

39 H 0.086197

40 H 0.085267

41 H 0.087447

42 H 0.086971

43 H 0.091422

44 H 0.086344

45 H 0.087017

46 H 0.086963

47 H 0.087388

48 H 0.086829

49 H 0.086731

50 H 0.086761

51 H 0.086614

52 H 0.086683

53 H 0.090653

54 H 0.090662

55 H 0.090741

56 H 0.090732

57 H 0.098707

58 H 0.101293

59 H 0.101330

60 H 0.098700

61 H 0.101235

62 H 0.101289

Table 3

Atom charges (with hydrogen charges calculated in) of C20H42

Label Atom Charges

1 C 20.001516

2 C 0.000292

3 C 0.006377

4 C 0.000474

5 C 20.005926

6 C 0.006178

7 C 20.005752

8 C 20.005879

9 C 0.006496

10 C 20.005751

11 C 20.000131

12 C 0.006144

13 C 20.000520

14 C 0.000406

15 C 0.008146

16 C 0.007221

17 C 0.007906

18 C 0.008059

19 C 20.016125

20 C 20.016098

J. Zhang et al. / Fuel 83 (2004) 315–326318

(3) Carbon atoms on the two ends of –CyC demonstrate

different electron properties: the end carbon atom C (6)

has some electronegativity while C (3) has relatively

strong electropositivity affected by the neighbor

oxygen atom O (1). The significant difference of their

charges will bring some polarity to the double bond.

3.1.3. DFT calculation of oligopolymer of EVA

Solvent effect calculation will give some useful infor-

mation of the PPD molecules in the solution. The

calculation of solution is quite exhausting of time and

computer internal memory, and too complicated systems

will make the calculation hard to converge. Therefore, the

oligopolymer of EVA is selected as the representative of the

EVA molecules with high molecular weight. The study

results proved that it could also give enough information of

the static properties of the PPD molecule in solution.

The optimized structure in the solution and the label of the

atoms were shown in Fig. 3. The calculated structure

parameters and atom charges were listed with Tables 6 and 7.

The optimized energy in the calculating level of the

molecule in vacuum is 2464.965 a.u., and the dipole is

1.881 Debye. The two parameters of EVA in heptane

solvent is 2464.967 a.u. and the dipole is 2.033 Debye

calculated with PCM model.

From the results, several points can be summed up as

following:

(1) In the heptane solution, the optimized structure has

not obviously changed comparing to the molecule in

vacuum with the same original conformation. The

bonds have shrinked, and the bond angles and

dihedrals have changed to different extent. The

molecules are more compacted than those in vacuum.

Furthermore, the steric effect of solvent molecules

may also attribute to the structure changes, which

push the atoms closer.

(2) The atom charge calculation shows that the electro-

negativity of O (6) decreased a little, while that of O

(9) increased obviously, but their electronegativity

Table 4

Optimized structure parameter of vinyl acetate

Bond Distance

(Angstrom)

Angle Degree Dihedral Degree

R(1,2) 1.3747 A(2,1,3) 123.268 D(3,1,2,4) 23.4025

R(1,3) 1.3785 A(1,2,4) 118.2026 D(3,1,2,5) 177.0006

R(2,4) 1.5152 A(1,2,5) 117.8965 D(2,1,3,6) 164.4608

R(2,5) 1.2034 A(4,2,5) 123.8995 D(2,1,3,7) 217.7858

R(3,6) 1.3293 A(1,3,6) 120.4786 D(1,2,4,8) 66.3765

R(3,7) 1.085 A(1,3,7) 116.4142 D(1,2,4,9) 254.2523

R(4,8) 1.0961 A(6,3,7) 123.0666 D(1,2,4,10) 2174.5523

R(4,9) 1.0951 A(2,4,8) 111.3301 D(5,2,4,8) 2114.0528

R(4,10) 1.09 A(2,4,9) 111.6707 D(5,2,4,9) 125.3185

R(6,11) 1.0837 A(2,4,10) 107.6195 D(5,2,4,10) 5.0185

R(6,12) 1.0847 A(8,4,9) 107.8613 D(1,3,6,11) 177.7375

A(8,4,10) 108.7402 D(1,3,6,12) 21.791

A(9,4,10) 109.5784 D(7,3,6,11) 0.1385

A(3,6,11) 119.8773 D(7,3,6,12) 2179.3901

A(3,6,12) 121.517

A(11,6,12) 118.604

Table 5

Optimized atom charges of vinyl acetate

Charges of atoms Charges with hydrogen charges

calculated in

Label Atom Charges Label Atom Charges

1 O 20.432686 1 O 20.432686

2 C 0.600304 2 C 0.600304

3 C 0.154716 3 C 0.302778

4 C 20.565163 4 C 0.005742

5 O 20.424648 5 O 20.424648

6 C 20.372994 6 C 20.051490

7 H 0.148062

8 H 0.177551

9 H 0.192377

10 H 0.200977

11 H 0.153252

12 H 0.168253

Fig. 2. The DFT optimized structure of EVA molecule in vacuum.

Fig. 3. The DFT optimized structure and atom labels of EVA monomer in

heptane.

J. Zhang et al. / Fuel 83 (2004) 315–326 319

was still higher than that of the carbon atoms, and

the polarity difference between O and C atoms is

obvious.

Owing to the changes of electron atmosphere brought by

the heptane solvent, the charge distribution of the carbon

and hydrogen atoms has changed much, too. Some of the

electronegativity of the carbon atoms (C (1), C (2), C (4),

C (7), C (8)) with the charges of hydrogen atoms calculated

in has been enhanced.

It educes that when EVA is in heptane, there is obvious

polarity difference between the ester groups of EVA and

heptane, paralleling with that, the non-polarity part on the

main chain of EVA molecule is affected little by the

solvent and has an excellent affinity with the alkane

molecules. The polarity difference between the O atoms

Table 6

The optimize parameters of EVA molecular in vacuum and heptane

L Bond Vacuum Heptane L Bond Vacuum Heptane L Bond Vacuum Heptane

R1 R(1,2) 1.5317 1.5301 A1 A(2,1,11) 110.7599 110.5888 D1 D(11,1,2,3) 2177.075 2175.6869

R2 R(1,11) 1.0955 1.0961 A2 A(2,1,12) 111.1847 111.4753 D2 D(11,1,2,14) 60.3439 61.5663

R3 R(1,12) 1.095 1.0951 A3 A(2,1,13) 111.3307 111.4736 D3 D(11,1,2,15) 256.493 255.1271

R4 R(1,13) 1.0959 1.0954 A4 A(11,1,12) 107.6384 107.4017 D4 D(12,1,2,3) 63.2917 64.9005

R5 R(2,3) 1.5307 1.5296 A5 A(11,1,13) 108.0397 108.0227 D5 D(12,1,2,14) 259.2894 257.8463

R6 R(2,14) 1.0984 1.0981 A6 A(12,1,13) 107.7306 107.7046 D6 D(12,1,2,15) 2176.1263 2174.5397

R7 R(2,15) 1.0983 1.0979 A7 A(1,2,3) 114.1595 114.3959 D7 D(13,1,2,3) 256.8393 255.4929

R8 R(3,4) 1.5299 1.5276 A8 A(1,2,14) 109.9917 109.9859 D8 D(13,1,2,14) 2179.4205 2178.2397

R9 R(3,6) 1.4587 1.4596 A9 A(1,2,15) 109.6479 109.5738 D9 D(13,1,2,15) 63.7427 65.0669

R10 R(3,16) 1.0941 1.0941 A10 A(3,2,14) 108.7715 108.7713 D10 D(1,2,3,4) 178.7382 178.7065

R11 R(4,5) 1.5336 1.5316 A11 A(3,2,15) 107.4314 107.3318 D11 D(1,2,3,6) 262.1259 262.4168

R12 R(4,17) 1.0992 1.0989 A12 A(14,2,15) 106.5345 106.4549 D12 D(1,2,3,16) 54.7997 54.7568

R13 R(4,18) 1.0992 1.0987 A13 A(2,3,4) 113.0292 112.9487 D13 D(14,2,3,4) 258.0174 257.8907

R14 R(5,10) 1.5321 1.5301 A14 A(2,3,6) 108.2263 108.7861 D14 D(14,2,3,6) 61.1185 60.986

R15 R(5,19) 1.0987 1.0992 A15 A(2,3,16) 110.0919 109.9311 D15 D(14,2,3,16) 178.044 178.1596

R16 R(5,20) 1.0971 1.0972 A16 A(4,3,6) 107.6526 107.1845 D16 D(15,2,3,4) 56.9285 56.9103

R17 R(6,7) 1.3551 1.3516 A17 A(4,3,16) 110.3743 110.5208 D17 D(15,2,3,6) 176.0645 175.787

R18 R(7,8) 1.5126 1.5101 A18 A(6,3,16) 107.247 107.2585 D18 D(15,2,3,16) 267.01 267.0394

R19 Rð7; 9Þ 1.2116 1.2128 A19 A(3,4,5) 114.3982 114.3632 D19 D(2,3,4,5) 2177.4071 2177.4469

R20 R(8,21) 1.0905 1.0905 A20 A(3,4,17) 108.8543 108.9228 D20 D(2,3,4,17) 59.3716 59.2553

R21 R(8,22) 1.0948 1.0948 A21 A(3,4,18) 107.6178 107.5729 D21 D(2,3,4,18) 255.6362 255.6948

R22 R(8,23) 1.0952 1.0952 A22 A(5,4,17) 109.7968 109.8341 D22 D(6,3,4,5) 63.126 62.7513

R23 R(10,24) 1.0958 1.0961 A23 A(5,4,18) 109.3896 109.4183 D23 D(6,3,4,17) 260.0953 260.5464

R24 R(10,25) 1.097 1.0972 A24 A(17,4,18) 106.4683 106.4095 D24 D(6,3,4,18) 2175.1031 2175.4966

R25 R(10,26) 1.0971 1.0973 A25 A(4,5,10) 112.7457 112.7423 D25 D(16,3,4,5) 253.6237 253.8219... ..

. ... ..

. ... ..

. ... ..

.

A32 A(6,7,8) 110.253 110.4669 D32 D(3,4,5,19) 55.8875 56.2118

A33 A(6,7,9) 124.7811 124.6361 D33 D(3,4,5,20) 260.0179 259.728

A34 A(8,7,9) 124.9656 124.8968 D34 D(17,4,5,10) 259.1883 258.9271

A35 A(7,8,21) 109.4689 109.6268 D35 D(17,4,5,19) 178.5992 179.017

A36 A(7,8,22) 110.2444 110.3286 D36 D(17,4,5,20) 62.6938 63.0772

A37 A(7,8,23) 110.0276 110.1201 D37 D(18,4,5,10) 57.3051 57.5333

A38 A(21,8,22) 110.0252 109.8755 D38 D(18,4,5,19) 264.9074 264.5226

A39 A(21,8,23) 109.792 109.6586 D39 D(18,4,5,20) 179.1872 179.5376

A40 A(22,8,23) 107.2568 107.1984 D40 D(4,5,10,24) 179.6687 179.6146

A41 A(5,10,24) 111.283 111.3475 D41 D(4,5,10,25) 59.603 59.5689

A42 A(5,10,25) 111.2174 111.2674 D42 D(4,5,10,26) 260.2514 260.3028

A43 A(5,10,26) 111.2908 111.3543 D43 D(19,5,10,24) 258.2844 258.442

A44 A(24,10,25) 107.687 107.6103 D44 D(19,5,10,25) 2178.3501 2178.4877

A45 A(24,10,26) 107.6591 107.593 D45 D(19,5,10,26) 61.7955 61.6406

A46 A(25,10,26) 107.5161 107.4694 D46 D(20,5,10,24) 57.9656 57.7941

D47 D(20,5,10,25) 262.1001 262.2516

D48 D(20,5,10,26) 178.0454 177.8767

D49 D(3,6,7,8) 179.3281 178.8346

D50 D(3,6,7,9) 20.4781 21.0329

D51 D(6,7,8,21) 177.9389 177.8096

D52 D(6,7,8,22) 56.7748 56.6756

D53 D(6,7,8,23) 261.3229 261.4585

D54 D(9,7,8,21) 22.2553 22.3234

D55 D(9,7,8,22) 2123.4194 2123.4573

D56 D(9,7,8,23) 118.4829 118.4085

J. Zhang et al. / Fuel 83 (2004) 315–326320

and non-polar alkane molecules makes them show strong

repulsion effect.

(3) The dipole of EVA molecule has decreased comparing

with that of VA molecule, which indicates that when –

CyC is opened and non-polar part is polymerized on

VA, the polarity of the molecule is lowered obviously.

(4) The dipole of EVA in heptane has increased a little than

EVA in vacuum, which reveals that the polarity

difference between EVA and heptane is more obvious

than that between EVA and vacuum.

Though the polarity difference between the ester groups

and the alkane chains is obvious, the dipole or polarity of the

whole molecule will be decreased by the non-polar parts of

EVA molecule (the alkane parts). Then the not so obvious

polarity of the EVA molecule will make it easier to mix well

with oils and bring excellent effect to the growing wax

crystals. However, the polarity difference between the ester

groups and alkane chains still exist in local parts of EVA

chain, which assures the good hindering effect to the

enlarging of (001) plane of the wax.

3.2. MM calculation

In this section, EVA in vacuum with a random original

conformation, 2000 molecule weight and 25% of acetate

were used as the main character in the calculation.

3.2.1. Molecular mechanics property of PPD molecules

The optimized structure of EVA molecule with random

conformation is shown in Fig. 4, and the MM optimized

structure of normal alkane molecules with random confor-

mation has also been calculated (Fig. 5).

With the contrastive results, it was found that when the

polar groups were introduced into EVA molecule, the

carbon bonds neighboring to the ester groups on the main

chain have performed well rigidity. We have also

optimized EVA molecular structure with other initial

conformation, and all the results showed that the carbon

bonds neighboring to the ester groups on the main chain

of EVA always kept about 1108, while the common

similar alkane molecules with no polar groups would twist

in relatively random sites of the main chain. Then it can

be concluded that the introduction of the polar groups has

enhanced the rigidity of the main chain of this

oligopolymer.

In our study, EVA molecules are divided into chain

sections, which are separated by the polar ester groups.

Every chain segment has a certain number of carbon atoms.

When EVA interacting with the wax crystals, the rigidity

brought by the polar groups conduces EVA to keep

relatively straight on joint points of the segments. Because

the non-polar part of one chain segment orientates with the

n-alkane molecules of the wax crystals for the similarity

between them and form straight chain like the alkane

molecules, the rigidity helps the next non-polar chain

Table 7

Optimized charges of EVA in vacuum and heptane

Label Atom In vacuum In heptane (PCM model)

Charges Charges with H Charges Charges with H

1 C 20.451249 20.000614 20.450693 20.001142

2 C 20.258305 0.018495 20.260466 0.021547

3 C 0.109641 0.275514 0.111589 0.2742

4 C 20.257629 0.012963 20.260682 0.016256

5 C 20.256591 0.024303 20.256359 0.022282

6 O 20.471858 20.471858 20.470116 20.470116

7 C 0.608526 0.608526 0.612561 0.612561

8 C 20.525963 0.014436 20.528227 0.018913

9 O 20.467696 20.467696 20.480704 20.480704

10 C 20.443176 20.014068 20.443642 20.013796

11 H 0.144321 0.143214

12 H 0.149932 0.148111

13 H 0.156382 0.158227

14 H 0.139863 0.141245

15 H 0.136936 0.140768

16 H 0.165873 0.162611

17 H 0.137181 0.13911

18 H 0.133411 0.137828

19 H 0.140626 0.136907

20 H 0.140268 0.141733

21 H 0.181081 0.18109

22 H 0.179227 0.182542

23 H 0.180091 0.183507

24 H 0.145091 0.144457

25 H 0.142344 0.143021

26 H 0.141673 0.142368

J. Zhang et al. / Fuel 83 (2004) 315–326 321

segment of EVA molecule to get into next wax crystal unit

and accelerates the growth rate of (110) and (200) plane.

The growth rate of (001) plane is cumbered for the polar

ester groups. Additionally the alkane molecules with long

carbon chain, which is easy to form coiled or folded chain

structure, is easy to crystallize with the wax and growth on

(110) and (200) plane to accelerate the growth of (001)

plane.

3.2.2. MM calculation of coexisting system of PPD and

normal alkane molecules

To get a clearer image of the interaction between EVA

and n-alkane molecules of the wax crystals, we have carried

out some calculation of the coexisting systems with alkane

molecules on different positions beside the EVA molecule.

There must be a lot of conformations of EVA in different

environments, but here, for simplification and obtaining a

clear image, a straight EVA molecule can be selected for the

interaction calculation with MM method. The results are

shown in Fig. 6.

From the three figures, we can find out that:

(1) When the molecule systems established equilibrium in

the force field, the non-polar parts of EVA molecules

performed excellent affinity with the alkane molecules

around, and kept the distance between them with about

4.3 A in 3D (the distance is calculated and averaged

between the carbon backbones in 3D for each alkane

molecule parts with no obvious influence brought by

the polar parts of the EVA molecule). The molecules

with the similar polarity formed parallel chain

structure.

(2) The polar part has shown a significant repulsion effect

to the n-alkane molecules, especially the methyl end of

the alkane molecules and the polar ester groups of

EVA. We have noted that, in the DFT calculation, the

electron density of the methyl groups is higher than

that of methylene groups on the carbon chain of alkane

molecules. Then this will give a good explain to this

stronger repulsion effect. But that does not mean that

there is little repulsion effect between the methylene

groups of alkane molecules and the polar groups of

EVA.

3.2.3. MM optimization of multi-molecule systems

In our study, the principle of the interaction between wax

crystals and the PPD molecules is desirably obtained, and

the impact on the alkane molecules in the solution made by

the PPD molecules on the crystal surface is also desirable.

Although the polar or non-polar properties of the single

molecules in the system was known, we still wanted to

know the property of the multi-molecule systems, including

the alkane and the PPD molecules, which might be similar

Fig. 4. MM optimized structure of PPD molecule with one random original structure got with single molecular MD calculation in vacuo.

Fig. 5. MM optimized structure of normal-alkane molecule with one random original structure got with MD calculation in vacuo.

J. Zhang et al. / Fuel 83 (2004) 315–326322

to the coexisting systems of the wax crystals and PPD

molecules.

Before calculating the coexisting system, the MM

calculation of the multi-alkane molecule system has been

completed to get some knowledge about the interaction

of the alkane molecules and the conformation of the

coexisting system. For selecting the initial conformation,

the XRD data from the Joint Committee on Powder

Diffraction Standards (JCPDS) and our last research [24]

need to be considered, and the same does to the crystal

parameters reported by other documents. Noticeably the

distance and position of the molecules were not quite

correct. To find more about this system, we have put

some molecules straight out the postulated (001) plane of

the crystal.

The MM optimized structure of this system is shown in

Figs. 7 and 8, which are the images from different

directions.

From the pictures, it appeared that when the molecules

moved to find their equilibrium position in the system, they

kept a good layer structure with interlayer distance of about

4.3 A, which was consistent with the XRD data and the

calculation above. From the projection along the chain

length of the alkane molecules, an orthorhombic crystal

structure of paraffin wax was found in our study, which also

agreed with the reported results.

The molecules extended straight out (001) plane has

also made efforts to find the equilibrium of their ends. From

the results it is found that the ends have bent their chain to

the other layers and want to keep the distance of 4.3 A as the

stable position where will let them have the minimum

potential energy.

Subsequently the coexisting system of PPD molecule

surrounded by some alkane molecules was calculated. The

optimized structure is shown in Fig. 9.

The picture presents the information that the affinity

between the non-polar segment of the EVA molecule and

alkane molecules. On one side of the carbon backbone of

EVA, which is opposite to the ester groups, the EVA

molecules hold a stable distance of about 4.3 A away to the

alkane molecules around. Thus it can be concluded that

the EVA molecules have enough affinity ability to attach to

the crystal plane and also have the ability to bond many

crystal units along the carbon backbone, which help the

growth of the planes perpendicular to (001) plane. As the

existence of the polarity difference between EVA and

alkane molecules, crystal surface may help to change the

surface tension distribution of the growing crystal units after

the PPD molecule absorbed onto the wax.

Paying attention to the side of ester groups, we find that

the distance between the EVA molecule and alkane

molecules neighboring to it has been changed into about

Fig. 6. The MM optimized structure of the simple coexisting system of alkane molecules and EVA molecules.

Fig. 7. The MM optimized structure of multi-alkane molecule system.

J. Zhang et al. / Fuel 83 (2004) 315–326 323

5.8 A, which is much further than the distance of the alkane

molecules or the interplanar distance of wax crystals. This

significant change will bend the alkane molecules to attach

to the wax crystal surfaces. Furthermore, it is found that the

non-polar segment of EVA molecule has good affinity to

the alkane molecules, from which it can be concluded that

the bent alkane molecule will also attach to the wax crystal

surface with the parts a bit farther to the ester groups of EVA

molecule. But the bent alkane molecules along the wax

crystal surface will give more obstacles to the alkane

molecules in the solution to deposit on the crystal with steric

hindrance effect. From the DFT calculation, it is known that

the methyl groups on the end of the alkane molecules have

higher electronegativity and can give more repulsion effect

to the other alkane molecules, which will get nearer to it.

The information why the growth of (001) plane is

hindered is given, and it can be summarized that the steric

hindrance effect bent alkane molecules is the powerful

explanation to the good performance effect of PPDs with

only relatively low concentration in the oils.

Moreover, when PPDs are added into the oils, the growth

in 3D will be uniformed to some extent.

3.3. Further discussion

From the results and discussion of the DFT and MM

calculation, we can conclude that the polar groups in the

PPD molecule have a suitable distribution, content and

conformation to performance well in the oils.

For holding back the alkane molecules to deposit onto the

wax crystals through using PPD molecules, the non-polar

part of EVA, which has good affinity to the alkane

molecules, should be shorter than the alkane molecules in

the oil. In other words the carbon segment of EVA molecule

should have fewer carbon atoms than most of the alkane

molecules of the wax crystals. Only in such instance, the

alkane molecules adsorbed onto the wax crystal surface near

the PPD molecule will bend well to bring steric hindrance to

the deposition of other molecules on the surface around.

As we know, the polar difference between ester groups

and carbon chains is great. If there are too many such polar

groups, the PPD molecules must have little affinity to the

wax crystals and the solubility of PPD in the oil will turn

hard. If the PPD molecule cannot attach to the crystal or

Fig. 8. The projection of the system of Fig. 7 along the axis of alkane

molecular chains.

Fig. 9. The MM optimized structure of the complex coexisting system of alkane molecules and an EVA molecule.

J. Zhang et al. / Fuel 83 (2004) 315–326324

even not be mixed with the oil uniformly, the lower of the

cold filtering plugging point (CFPP) of the diesel oils may

be hard to find, well then the carbon atoms in each carbon

segment of EVA molecules should be not much fewer than

most of the alkane molecules to deposit onto the wax

crystals.

Thereby a kind of PPD with suitable carbon atoms in

each carbon segment is required, which is divided by the

ester groups to give a good performance in lowering CFPP.

We know that in the diesel oils, the average carbon number

of the alkane molecules composing the wax crystals is about

20, and the carbon number of the carbon segment of EVA

molecules is determined by the acetate content. The

relationship between the carbon number of the segment of

PPD chain and acetate percent of EVA has been calculated,

as shown in Fig. 10.

From Fig. 10, we find that the acetate percent should be

about 30%, and the concrete value should be determined in

the experiment. This value is well consistent with our

experimental results or other published results [25].

In this article, solvent effect by the diesel fuels was

discussed and heptane was used as the model oil. The

real oil is a complicated mixture of saturate, aromatic

and heteroatomic compounds, so the performance mech-

anism of the PPD will also be affected by the compounds

in the oil. Nevertheless, the interaction between the wax

crystals and EVA molecules will be much more

important in low temperature when the wax crystals are

growing large, the study on the simplified systems still

will give important results which are helpful to under-

stand the performance mechanism of PPDs. In the later

study, good oil models will give more valuable

conclusions in the future days.

4. Conclusions

The DFT and MM calculation have given us some direct

information about the interactions between EVA and

n-alkane molecules in the wax or on the crystal units.

From the results and discussion above, some conclusions

are drawn as below:

(1) The alkane molecule is a non-polar molecule, but

the methyl groups on the end of the molecule have

higher electronegativity than all the methylene

groups in it.

(2) In the polymer of EVA, it has some polarity, but

the polarity of the whole molecule has decreased

much more than VA because of the introduction

of ethylene monomers. The results also show

that the polar groups, i.e. the ester groups, have

higher polarity in the solution than in vacuum.

The EVA molecule is divided into segments by

the ester groups. The introduction of the polar parts

has improved the rigidity of the neighboring carbon

bonds on the backbone chain of EVA. This will

help the EVA to get into the next wax crystal unit,

and bring the broadening of the planes perpendicular

to (001) plane of the crystal.

(3) The segments on the EVA molecules have quite

good affinity to the alkane molecules around, and

will attach the wax crystal surface easily. But the

polar groups will bring repulsion effect to the alkane

molecules to deposit on the wax crystal surface near

EVA. For there is still much affinity between EVA

molecule and alkane molecules, the alkane mol-

ecules will be absorbed on the surface with

bending conformation. This kind of conformation

will bring steric hindrance effect to the alkane

molecules to deposit on this area, and the

higher electronegativity will also bring electronega-

tivity to the alkane molecules in the solution. This

will help prevent the high broadening velocity of

(001) plane.

(4) Considering the requirement of polarity and affinity

to the alkane molecules of the EVA molecules, we

think that the carbon atom number of the segments

of EVA molecules should be lower than the mean

carbon atom number of the alkane molecules

composing the wax crystals. Then we calculated

that the acetate content of the EVA molecule should

be about 30% and the concrete value should be

determined by the experiment according to the

property of the oils to be used.

Acknowledgements

We would like to thank Professor P. Mark Rodger of

University of Warwick for providing their published articlesFig. 10. The relation between carbon number of segment of PPD chains and

acetate percent.

J. Zhang et al. / Fuel 83 (2004) 315–326 325

in this field, and Professor Kang Zhao of Tianjin University

for the English checking of this article. The support of the

Researching Institute of Yanshan refinery factory of

SinoPec is also appreciated.

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