Molecular dynamics simulation of poly(butyl) - Springer Link

2 downloads 0 Views 430KB Size Report
Nov 19, 2014 - Ul´yanovskaya, Petergof, 198504 St. Petersburg, Russian Federation. Fax: +7 (812) 428 7240. E mail: [email protected]. bInstitute of ...
Russian Chemical Bulletin, International Edition, Vol. 65, No. 1, pp. 67—74, January, 2016

67

Molecular dynamics simulation of poly(butyl)carbosilane dendrimer melts at 600 K A. N. Shishkin,a D. A. Markelov,a,b,c and V. V. Matveeva aFaculty

of Physics, St. Petersburg State University, 3 ul. Ul´yanovskaya, Petergof, 198504 St. Petersburg, Russian Federation. Fax: +7 (812) 428 7240. Email: [email protected] bInstitute of Macromolecular Compounds, Russian Academy of Sciences, 31 Bol´shoi prosp., 199004 St. Petersburg, Russian Federation. Fax: +7 (812) 328 6869 cSt. Petersburg National Research University of Informational Technologies, Mechanics, and Optics, 49 Konverksky prosp., 197101 St. Petersburg, Russian Federation The structural properties of melts of poly(butyl)carbosilane (PBC) dendrimers of the third (G3), fifth (G5), and sixth (G6) generations were studied by molecular dynamics simulation at 600 K. A substantial difference was found between the density of the melt of the G6 generation dendrimer and the densities of the melts of the G3 and G5 generation dendrimers. The ob tained computer simulation results do not confirm the hypothesis that these differences are caused by physical entanglements between the branches of the neighboring dendrimers (which take place for G6 to a higher extent) and indicate, most likely, the minimization of the inter dendrimer free volume due to a more regular packing. Key words: poly(butyl)carbosilane dendrimer, molecular dynamics, radial density profile.

Dendrimer is a regular treelike macromolecule with a wide set of unique properties different from the properties of other types of polymers. Dendrimers are utilized in var ious fields: polymer chemistry, biology, and medicine.1—3 The staged cascade synthesis makes it possible to ob tain macromolecules with the same size and structure.4—7 The chemical composition of dendrimers can be varied rather flexibly and makes it possible to synthesize macro molecules with different properties. Owing to the treelike structure, the dendrimer has many terminal functional groups, which can impart beforehand specified properties to the macromolecule.8 Melts of poly(butyl)carbosilane (PBC) dendrimers (1) and other types of carbosilane dendrimers were studied in recent experimental works in a wide temperature range (6—600 K) using different experimental methods: visco simetry, precision adiabatic vacuum and differential scan

ning calorimetry, dynamic light scattering, and atomic force microscopy.9—12 It was found that the thermodynamic properties of a melt of the sixth generation dendrimer (G6) differ sharply from similar properties of dendrimers with a lower num ber of generations, and these distinctions are most notice able at high temperatures.9 The same effect was observed for the carbosilane dendrimers with different terminal groups10 or with the modified core.11 It was assumed that this effect is related to the physical entanglement between macromolecules that appear only for dendrimers with a high number of generations.12 The purpose of this work is to study this effect by the computer simulation of the PBC dendrimers of different generations. We know only a few works in which the com puter simulation of dendrimer melts was performed. For example, melts of poly(propylene)amine dendrimers of

Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 1, pp. 0067—0074, January, 2016. 10665285/16/65010067 © 2016 Springer Science+Business Media, Inc.

68

Russ.Chem.Bull., Int.Ed., Vol. 65, No. 1, January, 2016

Shishkin et al.

the G2—G5 generations were studied13 at 400 K by mo lecular dynamics using the coarsegrained model. The pur pose of the work was to study the supramolecular structure of melts of dendrimers. It was established that the density profile of the dendrimer has a standard structure without cavities inside and the terminal groups are distributed over the whole volume of the macromolecule. It was shown that the mutual penetration of the dendrimers decreases with the number of generation and that the radius of gyra tion depends on the molecular weight as Rg ∼ M0.28. The molecular dynamics simulation was performed14 for melts of dendrimers of the G3 and G4 generations using the coarsegrained freely articulated model of a mac romolecule; i.e., the segment between branching nodes was simulated by two "rigid sticks." The structural and dynamic properties of the dendrimers were studied in the range from 260 to 750 K, including the properties of this melt in the range of glass transition temperature, which were studied in detail. Note that the Dreiding force field was used in these works13,14 for the simulation of melts of the dendrimers.15 The melt of PBC dendrimers with the G3, G5, and G6 generation with the functionality of the central node Fc = 4 and functionality of other branching nodes F = 3, i.e., dendrimers of the homological series 4—3, was studied in this work by molecular dynamics simulation using the atomistic model. The studies were mainly focused on the simulation results for this system at 600 K, since it is assumed that the most distinction of the properties of the G6 dendrimers from the properties of dendrimers of lower generations is observed at high temperatures. The used model of the macromolecule and simulation method are described in the first section. The simulation results are presented and the obtained results are discussed in the second section.

which designate sites of connection of this segment with segments of other generations, were specially marked in each segment. The bond linking the segment to the previ ous generation is marked by dashed line, and the terminal branching points linking the segment to the next genera tion are designated by a circle. These atoms are removed when the segments are joined into dendrimer. Dendrimer assembling started from core 2. Then internal segments 3 were attached to the core. The procedure was carried out (G – 1) times, and terminal segments 4 were attached at the last stage. At each stage, the energy was minimized using the Forcite module and the COMPASS force field incorporated into the MaterialsStudio program package. The assembled dendrimer was balanced by molecular dy namics simulation in vacuo for 100 ps also using the Forcite module and the COMPASS force field.

Model of dendrimer and simulation procedure

Preparation and simulation of a melt of the PBC den drimer at 600 K without electrostatic interactions. For the simulation of the melt, a cubic cell containing 27 den drimers (Fig. 1, b) was formed in the AmorphousCell mod ule of the MaterialsStudio 6.0 package. The average den sity of the cell was specified as 0.6 g cm–3. The cell used has periodical boundary conditions and cubic shape and is surrounded by its intrinsic images in such a way that the space would be filled without cavities providing an infinite system in all directions and excluding the surface layer effect. Then, the obtained configuration was exported for simulations in the Gromacs program.17 Energy minimization was performed to use the ob tained initial configuration of the system in the Gromacs package. Then this system was balanced by molecular dy namics simulation for at least 100 ps with an increment of 0.005 fs at 600 K (other simulation details will be de scribed below). Then the simulation increment was grad ually increased to 1 fs. Molecular dynamics simulation

Assembling of individual dendrimer. It is important that assembling of an individual dendrimer and a simulation cell of the melt and the further balancing of the system were performed without electrostatic interactions, i.e., at zero or "switchedoff" partial charges of atoms. Then the system was additionally balanced when simulating sys tems with partial charges. The MaterialsStudio 6.0 program package was used to form the structure of an individual dendrimer (Fig. 1, a).16 First, the PBC dendrimer was collected using the diver gent method in the BuildPolymers module of this pack age. At each step, the dendrimer of the G+1 generation was collected from the dendrimer of the G generation by the addition of segments. For this purpose, three types of segments of the PBC dendrimer were imported into this module: core (2), internal segment (3), and terminal seg ment (4). The hydrogen atoms of the branching points,

MD simulation of dendrimer melts at 600 K

Russ.Chem.Bull., Int.Ed., Vol. 65, No. 1, January, 2016

a

69

b

Fig. 1. Instant configuration of an individual PBC dendrimer of the G6 generation at T = 300 K (a) and a melt of the PBC dendrimers of the G6 generation at T = 600 K (b).

was performed in the NPT ensemble in the Gromacs pack age (version 4.5.5). The Berendsen barostat18 and Vres cale thermostat19 were used for all systems. The LINCS algorithm20 served to maintain the established bond lengths and bond and torsion angles. Mixing procedure was carried out for the system to "forget" the initial configuration. It is necessary for suffi cient mixing that an individual dendrimer would shift by a distance equal to or longer than the radius of gyra tion (Rg). For this purpose, melts of dendrimers were simulated without electrostatic interactions for 20 ns, which, as can be seen from Fig. 2, allows the mean square displacement (MSD) for each dendrimer would be equal to or exceed Rg2. The obtained final config urations were used for the simulation of equilibrium trajectories and as initial configuration for simula tion taking into account the electrostatic interaction (see below). Simulation of a melt of the PBC dendrimer at 600 K taking into account partial charges. The partial charges of atoms were calculated using the MaterialsStudio 6.0 pack age in the DMol3 module. The Hartree—Fock method with the dnp basis set (which is similar to the 631G** basis set in the Gaussian program)21 and the gradient cor rection method22 with the Perdew and Wang correction23 were used. The charges were calculated in the RESP ap proximation.24 Note that in this work we used the atomis tic model of joined atoms in which the groups of atoms СН2 or Me are simulated as a single atom with the total atomic weight of this group and, therefore, the charges for these groups were summated. The calculated charges for each group were averaged over atoms that are equally structurally remote from the dendrimer core and

approximated to 0.01 e. The used charged are presented in Table 1. For the simulation of melts of the PBC dendrimers, we used the final configuration obtained for the system with out partial charges; i.e., after mixing the systems, the elec trostatic interaction was "switchedon" in them and was took into account by the Ewald method using the PME algorithm.25 First, the simulation increment was decreased to 0.05 fs and simulation was carried out for at least 0.5 ns. Then the simulation increment was increased to 1 fs, and the system was balanced for 5 ns for the G3 and G5 den drimers and for 20 ns for G6. The equilibrium configura MSD/nm2, R 2g/nm2 10

1

2

3

1

101

102

103

104

t/ps

Fig. 2. Meansquare displacements of the PBC dendrimers of the generations G3 (1), G5 (2), and G6 (3) in a melt without electrostatic interactions as functions of time (dashed lines) and the dependence of the squared radius of gyration (R2g) of the dendrimers on the simulation time (solid lines).

70

Russ.Chem.Bull., Int.Ed., Vol. 65, No. 1, January, 2016

Table 1. Atomic weights and partial charges of atoms used in the molecular dynamics simulation of compound 1

Shishkin et al.

ρ/kg m–3

800 Atom/ joined atom

Type

m/amu

qresp*/e

1 2 3 4 5 6 7 8 9 10 11 12 13

Si Si Si Me Me Me CH2 CH2 CH2 CH2 CH2 CH2 CH2

28.080 28.080 28.080 15.035 15.035 15.035 14.027 14.027 14.027 14.027 14.027 14.027 14.027

0.84 0.95 0.95 –0.32 –0.32 –0.11 –0.21 0.00 –0.21 0.00 –0.21 0.00 0.11

2

1

760

3

5 6

4 720 1•104

2•104

t/ps

Fig. 3. Time dependences of the density at different pressures taking into account the electrostatic interaction in the cycle 1 atm (1)—100 atm (2)—1 atm (3) for the G5 dendrimer and in the cycle 1 atm (4)—100 atm (5)—1 atm (6) for the G6 dendrimer.

* Charge calculated in the RESP approximation.

tion of all simulated systems was considered to be achieved if the following physical magnitudes reached constant (av erage) values: — density of the system; — radius of gyration of the macromolecule; — average distance between the terminal groups; — potential energy of the system as a whole and its components: the van der Waals energy and energy of the electrostatic interaction. Simulation under a pressure of 100 atm for 10 ns was performed for each system as an additional checking that the balanced configurations of melts were achieved. Then the pressure was returned to 1 atm and the simulation was performed at which the system was balanced for 10 ns. No changes in the density of the melt, radius of gyration, and radial density profile were observed. The change in the density of melts of the G5 and G6 dendrimers during this cycle are presented in Fig. 3. After the described procedure of system balancing, the balanced simulation trajectories were obtained. They were not shorter than 20 ns for the melt of each PBC dendrimer (G3, G5, and G6) taking into account the electrostatic interaction. It is important to mention that the Dreiding force field, which has previously been used for the simulation of melts of other dendrimer types,13,14 for the PBC dendrimer re sulted in a higher density at 600 K than the experimental density of the melt at room temperature. Therefore, the Gromos53a6 force field, which, as will be shown below, gives the values of density of the PBC dendrimers consis tent with the experimental data,26 was chosen in this work. The system was cooled from 600 to 300 K with a step of 20 K for comparison with the experimental values of density of the studied melts,26 which are known only at 300 K. At each cooling step, the system was simulated for 2 ns for the G3 and G5 dendrimers and for 5 ns for G6.

The dynamics of the balancing process showed that these times are sufficient to reaching equilibrium values of den sity of the melt and radius of gyration. The temperature dependence of the density of the melts of the PBC den drimers is shown in Fig. 4. Almost all dependences are linear. A slight break is observed for the G6 dendrimer at 320 K. This break is insignificant in amplitude and corresponds to the change in density by less than 2% of the density value at 300 K. The effect is retained when both decreasing the cooling step to 10 K and increasing the length of the simulation projection at a given temperature to 20 ns. No hysteresis is observed for this dependence. Since this work is aimed at comparing the properties of melts of the dendrimers at 600 K, the temperature dependence of the density of the melts will not be discussed further.

ρ/kg m–3

900

G3 G5 G6

850

800

750

700 300

400

500

600

T/К

Fig. 4. Temperature dependence of the density of the melts of the PBC dendrimers.

MD simulation of dendrimer melts at 600 K

Russ.Chem.Bull., Int.Ed., Vol. 65, No. 1, January, 2016

The obtained values of density presented in Table 2 show that at 300 K the divergence between the density values obtained by the simulation using the electrostatic interaction and experimental values is lower than 1%. Thus, the method used and simulation parameters make it possible to describe correctly the physical properties of the melt of the PBC dendrimer. Results and Discussion The following characteristics were considered for anal ysis of the structural properties of the melt of the carbo silane dendrimers: density of the dendrimer melt (ρ0), ra dial density profile for one dendrimer (ρD), and radius of gyration of the dendrimer (Rg). In addition, the deviation of the shape of an individual dendrimer from the spherical shape and the degree of penetration of the dendrimers into each other are considered. The density of the dendrimer melt was calculated from the simulation data using the equation ρ0 = 27MD/(NA),

ρD(r) = /V(r),

(2)

where ρD(r) is the average density in the spherical layer at the distance r from the center of mass, is the aver Table 2. Density of the dendrimer (ρ) at 300 and 600 K and the asymmetricity parameter (δ) of the spherical shape of the dendrimer at 600 K (molecular dynamics simulation results)

3 5 6 7

MD /a.e.м. 14241 17904 36120 —

ρ/kg m–3

ρD/g cm–3

a

2

1

1

2

1

3

2

3

ρend/g cm–3

r/nm

b

1.0

0.5

δ

300 K

600 K

878±2 (878*) 882±1 (888*) 884±1 873*

716±6 728±3 783±2 —

* Experimental data.26

age total mass of atoms in the layer of the V(r) volume, has the dependence typical of dendrimers (Fig. 5). First, a sharp decrease in the density related to the formal mathe matical definition of this function occurs for all dendri mers. Then, a plateau is observed on which the density remains almost unchanged. Finally, ρD(r) decreases to zero at the periphery. Note that a similar structure of the radial density profile was obtained, in particular, for the carbosi lane dendrimer in solution.27 The dependence of the radius of gyration of the den drimer on the molecular weight is presented in Fig. 6. According to the theory,28 log(R g) as a function of log(MD•G2) is linear for a "good" solvent with a slope of ∼0.2. In the case of the θsolvent, the slope of this function should be ∼0.25. In the case of a "bad" solvent, log(Rg) as a function of log(MD) is linear with a slope of 0.28—0.33. Taking into account a sufficient penetration of the den drimers into each other (see Fig. 1, b), one should ex pect the behavior of this dependence as that in the θsolvent. However, the slope of the log(Rg) function to

(1)

where MD is the molecular weight of the dendrimer, is the volume of the simulation cell averaged over time for the equilibrium region of the trajectory, and NA is Avog adro´s number. As can be seen from the data in Table 2, at 600 K the density of the G6 dendrimer differs by more than 11% from the density of the dendrimers G3 and G5. At the same time, differences in densities of the melt for the same dendrimers at 300 K do not exceed 1%. It is important that, in spite of a high difference in densities of the G6 dendrimer and G5 and G3 dendrimers, no specific features of the structure or conformation are observed for the melt of the G6 dendrimer. For example, the radial density profile (ρD) calculated by the equation

G

71

1 4.4•10–4 2.5•10–4 0.9•10–4 —

1

2

2

3

3

r/nm

Fig. 5. Radial profile of the density for the dendrimers G3 (1), G5 (2), and G6 (3) taking into account the electrostatic interac tion at T = 600 K as a whole (a) and for the terminal groups (b).

72

Russ.Chem.Bull., Int.Ed., Vol. 65, No. 1, January, 2016

Rg/nm

a

Shishkin et al.

I1 = λ 1 + λ 2 + λ 3,

(5)

I2 = λ1λ2 + λ2λ3 + λ1λ3.

(6)

3 2

1

1•104

1•105

1•106 G2MD/amu

Rg/nm

b

3 2

1

1•104

1•105 MD/amu

Fig. 6. Radius of gyration of the dendrimers (Rg) vs molecular weight at T = 600 K.

the log(MD•G2) axis is 0.18 (see Fig. 6, a), which differs strongly from theoretical predictions. At the same time, the dependence of Rg for the melt of the PBC dendrimer is similar to that in the "bad" solvent. The dependence of log(Rg) on log(MD) is close to linear has a slope of 0.29. Most likely, this behavior is related to steric hindrance of dendrimer macromolecules, whose shape cannot differ strongly from the spherical shape. Note that similar re sults were obtained13 by the simulation of the melt of poly(propylene)imine dendrimers, where Rg ∼ MD0.28. The deviation of the dendrimer shape can be estimated using the Г tensor with the components

The value δ = 0 corresponds to the spherical shape of the macromolecule, and δ = 1 corresponds to the macro molecule with the extended and rigid shape. For the stud ied cases, the values of δ were obtained from the simula tion data with averaging over the whole equilibrium tra jectory. The values of λ2/λ1 and λ3/λ1 are presented in Fig. 7. The calculated δ values are listed in Table 2. As can be seen from the tabulated data, δ decreases for the G6 dendrimer compared to G3, indicating a more spherical shape of dendrimers with a higher number of generations. However, the shape of all dendrimers in the melt is any way close to the spherical one, since the δ parameter does not exceed the value of 5•10–4 for all generations. It is noteworthy that the relative penetration of den drimer macromolecules into each other diminishes with an increase in the number of generations in the dendrimer. To illustrate this fact, the degree of penetration of the dendrimers into each other (Joverlap) is presented in Fig. 8. This value is determined by the ratio of the weight of the atoms of neighboring macromolecules penetrating into the dendrimer to the weight of the dendrimer. The penetrat ing atoms in the sphere with the radius R relative to the center of mass of the dendrimer are taken into account (R = (5/3)0.5Rg corresponds to the radius of a ball with the uniform weight distribution and radius of gyration of the ball Rg). It should be emphasized that a similar situation was observed earlier for the simulation of the melt of the poly(amido)amine dendrimers.13 Thus, it seems natural to assume that the dependence of Rg on the molecular weight (which is similar to that for the macromolecules in the "bad" solvent) is due to diminishing penetration of the macromolecules into each other and retaining the spherical shape of the dendrimer. these factors should draw the dependence of Rg on the molecular weight to the dependence for the solid sphere (Rg ∼ (MD)0.33). λ2/λ1, λ3/λ1

1.1 ,

(3)

where u and v are indices of the Cartesian coordinates, rui is the component of the radiusvector for the ith atom along the u axis, and Ru is the component of the radius vector directed from the center of mass of the dendrimer along the u axis. Reducing the tensor to the diagonal form, we can find three eigenvalues (λ1, λ2, λ3), which are lengths of three major axes of ellipsoid. Asphericity of the macro molecule shape is characterized, as a rule, using δ, which is specified by the following equations29: δ = 1 – 3/,

(4)

1 0.9

2

0.7

3

4

5

6

G

Fig. 7. Dependences of λ2/λ1 (1) and λ3/λ1 (2) vs number of generation of the PBC dendrimers.

MD simulation of dendrimer melts at 600 K

Russ.Chem.Bull., Int.Ed., Vol. 65, No. 1, January, 2016

Joverlap

73

PSi 4

0.6

3

0.4

2 0.2 1 3

4

5

6

1

2

3

G

Fig. 8. Ratio of the weight of neighboring macromolecules penet rating into the dendrimer to the weight of the dendrimer (Joverlap) vs number of generation of the PBC dendrimers at T = 600 K.

To conclude, the shape of the dendrimer remains almost spherical with an increase in the number of gener ations. The penetration of other macromolecules into the dendrimer diminishes, and this result does not confirm the hypothesis that the difference in structures of the melt of the PBC dendrimers G6 from dendrimers with lower generations is caused by physical entanglements of branch es of different macromolecules. We could not find confir mation of this hypothesis by considering all possible pair functions for atoms belonging to different dendrimers. It can be assumed that distinctions of the melt of the PBC dendrimer G6 are associated with the necessity to minimize the interdendrimer free volume (i.e., necessity to fill the intermolecular space to the average density of the melt) rather than the penetration of the dendrimers into each other. The shape of dendrimers, which is close to the spherical one, does not allow the filling of this space in the absence of dendrimer penetration into each other. most likely, in the case of low generations, the available penetration is enough to prevent the formation of inter denrimer cavities, whereas for the G6 dendrimer the de gree of interpenetration becomes insufficient. this factor can be compensated using a more ordered arrangement of the dendrimers in the melt, i.e., by a denser packing of these macromolecules. In other words, the ordered ar rangement of the dendrimers in the melt would be caused by the efficient "suction" of the dendrimers to each other in the region of potential formation of a cavity. The posi tion of the central silicon atom in the dendrimer almost coincides with the position of the center of mass of the macromolecule, which is a consequence of the spherical shape of the macromolecule and treelike structure of the dendrimer. Therefore, to establish the existence of order in a melt of dendrimers, we calculated the pair radial dis tribution functions for the central silicon atoms: PSi(r). The obtained pair distribution functions are presented in Fig. 9. As can be seen, PSi for G3 has the broadest distri

1

2

r/Rg

Fig. 9. Pair distribution functions for the central silicon atoms (PSi) of the dendrimers G3 (1), G5 (2), and G6 (3) at T = 600 K.

bution with maxima at ∼2.1 Rg, indicating the absence of ordering in the arrangement of the dendrimers in the melt. For the G5 dendrimer, this distribution narrows about the value of 2.2 Rg and its amplitude increases. In the case of the G6 dendrimer, several narrow peaks are observed in stead of one broad peak, indicating that the dendrimers are divided into several groups, which are arranged at almost equal distances from the chosen dendrimer. Therefore, we may conclude that the melt of the PBC dendrimer G6 has a more ordered packing of macromole cules, indicating in favor of the hypothesis about den drimer "suction" due to preventing the formation of inter molecular cavities. To summarize the obtained results, we conclude that a noticeable difference in the physical properties of the melt of the PBC dendrimer G6 compared to the dendri mers of lower generations was discovered by both simula tion and experiment. The obtained computer simulation data do not confirm the hypothesis that these differences are due to physical entanglements between branches of the neighboring molecules of dendrimers, and these en tanglements are more pronounced for the G6 dendrimer. On the contrary, the mutual penetration of dendrimers decreases with an increase in the number of generation, which prevents a stronger entanglement between the den drimers of the G6 generation compared to the G3 and G5 dendrimers. A more ordered structure of the melt of the G6 dendrimer indicates, most likely, the mechanism of minimization of the interdendrimer free volume. Addi tional studies and experimental measurements are required to answer this question. Computational resources and program packages were presented by the Computation Resource Center of the St. Petersburg State University. This work was financially supported by the Russian Foundation for Basic Research (Project No. 140300926)

74

Russ.Chem.Bull., Int.Ed., Vol. 65, No. 1, January, 2016

and financially supported in part by the Government of the Russian Federation (Grant 074U01). References 1. J. Frechet, D. Tomalia, Dendrimers and Other Dendritric Polymers, Wiley, New York, 2002. 2. A. M. Muzafarov, E. A. Rebrov, V. S. Papkov, Russ. Chem. Rev. (Engl. Transl.), 1991, 60, 1596 [Usp. Khim., 1991, 60, 1596]. 3. P. R. Dvornic, M. J. Owen, in SiliconContaining Dendritic Polymers, Springer, New York, 2009, p. 21. 4. C. Dufes, I. F. Uchegbu, A. G. Schutzlein, in Polymers in Drug Delivery, Boca Raton, CRC Press, 2006, p. 195. 5. F. Vogtle, G. Richardt, N. Werner, Dendrimer Chemistry: Concepts, Syntheses, Properties, Applications, Wiley, Wein heim, 2009. 6. A. M. Muzafarov, N. G. Vasilenko, Priroda [Russ. Nature], 2011, 6 (in Russian). 7. B. Rosen, C. Wilson, D. Wilson, M. Peterca, M. Imam, V. Percec, Chem. Rev., 2009, 109, 6275. 8. D. Astruc, E. Boisselier, C. Ornelas, Chem. Rev., 2010, 110, 1857. 9. N. N. Smirnova, O. V. Stepanova, T. A. Bykova, A. V. Mar kin, A. M. Muzafarov, E. A. Tatarinova, V. D. Myakushev, Thermochimica Acta, 2006, 440, 188. 10. A. S. Tereshchenko, G. S. Tupitsyna, E. A. Tatarinova, A. V. Bystrova, A. M. Muzafarov, N. N. Smirnova, A. V. Markin, Polym. Sci., Ser. B (Engl. Transl.), 2010, 52, 41 [Vysokomol. Soedin., Ser. B, 2010, 52, 132]. 11. N. N. Smirnova, A. V. Markin, Ya. S. Samosudova, G. M. Ignat´eva, A. M. Muzafarov, Russ. J. Phys. Chem. (Engl. Transl.), 2010, 84, 784 [Zh. Fiz. Khim., 2010, 84, 884]. 12. M. V. Mironova, A. V. Semakov, A. S. Tereshchenko, E. A. Tatarinova, E. V. Getmanova, A. M. Muzafarov, V. G. Kuli chikhin, Polym. Sci., Ser. B (Engl. Transl.), 2010, 52, 1156 [Vysokomol. Soedin., Ser. B, 2010, 52, 1960].

Shishkin et al.

13. N. Zacharopoulos, L. G. Economou, Macromolecules, 2002, 35, 1814. 14. K. Karatasos, Macromolecules, 2005, 38, 4472. 15. S. L. Mayo, B. D. Olafson, W. A. Goddard, J. Phys. Chem., 1990, 94, 8897. 16. http://cc.spbu.ru/ru/content/accelrysmaterialsstudio. 17. B. Hess, C. Kutzner, D. van der Spoel, E. Lindahl, J. Chem. Theory Comput., 2008, 4, 435. 18. H. Berendsen, J. Postma, W. Gunsteren, A. Dinola, J. Haak, J. Chem. Phys., 1984, 81, 3684. 19. G. Bussi, D. Donadio, M. Parrinello, J. Chem. Phys., 2007, 126, 014101. 20. B. Hess, H. Bekker, H. Berendsen, J. Fraaije, J. Comput. Chem.,1997, 18, 1463. 21. F. Jensen, Introduction to Computational Chemistry, John Wiley and Sons, West Susex, 2007. 22. A. V. Arbuznikov, J. Struct. Chem. (Engl. Transl.), 2007, 48, S1 [Zh. Strukt. Khim., 2007, 48, 5]. 23. J. Perdew, Y. Wang, Phys. Rev., 1992, 45, 13244. 24. J. Wang, P. Cieplak, P. Kollman, J. Comput. Chem., 2000, 21, 1049. 25. T. Darden, D. York, L. Pedersen, J. Chem. Phys., 1993, 98, 10089. 26. E. A. Tatarinova, E. A. Rebrov, V. D. Myakushev, I. B. Meshkov, N. V. Demchenko, A. V. Bystrova, O. V. Lebe deva, A. M. Muzafarov, Russ. Chem. Bull. (Engl. Transl.), 2004, 53, 2591 [Izv. Akad. Nauk, Ser. Khim., 2004, 2484]. 27. M. A. Mazo, M. Y. Shamaev, N. K. Balabaev, A. A. Darin skii, I. M. Neelov, Phys. Chem. Chem. Phys., 2004, 6, 1285. 28. J. S. Klos, J. U. Sommer, Polymer Sci. Ser. C, 2013, 55, 125. 29. J. Rudnick, G. Gaspari, J. Phys. A, 1986, 19, 191.

Received November 19, 2014; in revised form June 10, 2015