^{1}and G. Zifferer

^{1,a)}

### Abstract

A most promising off-lattice technique in order to simulate not only static but in addition dynamic behavior of linear and star-branched chains is the dissipative particle dynamics (DPD) method. In this model the atomistic representation of polymer molecules is replaced by a (coarse-grained) equivalent chain consisting of beads which are repulsive for each other in order to mimic the excluded volume effect (successive beads in addition are linked by springs). Likewise solvent molecules are combined to beads which in turn are repulsive for each other as well as for the polymer segments. The system is relaxed by molecular dynamics solving Newton’s laws under the influence of short ranged conservative forces (i.e., repulsion between nonbonded beads and a proper balance of repulsion and attraction between bonded segments) and dissipative forces due to friction between particles, the latter representing the thermostat in conjunction with proper random forces. A variation of the strength of the repulsion between different types of beads allows the simulation of any desired thermodynamic situation. Static and dynamic properties of isolated linear and star-branched chains embedded in athermal, exothermal, and endothermal solvent are presented and theta conditions are examined. The generally accepted scaling concept for athermal systems is fairly well reproduced by linear and star-branched DPD chains and theta conditions appear for a unique parameter independent of functionality as in the case of Monte Carlo simulations. Furthermore, the correspondence between DPD and Monte Carlo data referring to the shape of chains and stars is fairly well, too. For dilute solutions the Zimm behavior is expected for dynamic properties which is indeed realized in DPD systems.

We are grateful for funding from the Austrian Science Fund FWF (Grant No. P20124). Parts of these calculations were performed on the Schrödinger Linux Cluster of the University of Vienna which is gratefully acknowledged.

I. INTRODUCTION

II. COMPUTATIONAL METHOD

III. RESULTS AND DISCUSSION

A. Athermal systems

B. Theta systems

C. Size of DPD stars and chains

D. Shape of DPD stars and chains

E. Mobility of DPD stars and chains

IV. CONCLUSIONS

### Key Topics

- Solvents
- 25.0
- Polymers
- 24.0
- Monte Carlo methods
- 16.0
- Static properties
- 10.0
- Diffusion
- 8.0

## Figures

Log-log plots of (a) mean square radius of gyration, (b) mean square end-to-end distance, and (c) mean square center-to-end distance vs total number of bonds of linear chains (circles) and stars with (triangles), (inverted triangles), (squares) and (diamonds) arms. Athermal conditions . Straight lines result from linear regression ( and ); slopes for read as (a) 1.181, 1.177, 1.153, 1.178, and 1.162, (b) 1.191, 1.194, 1.153, 1.196, and 1.173, and (c) 1.177, 1.188, 1.163, 1.189, and 1.172. Broken lines calculated by Eq. (10) using data given in Table I.

Log-log plots of (a) mean square radius of gyration, (b) mean square end-to-end distance, and (c) mean square center-to-end distance vs total number of bonds of linear chains (circles) and stars with (triangles), (inverted triangles), (squares) and (diamonds) arms. Athermal conditions . Straight lines result from linear regression ( and ); slopes for read as (a) 1.181, 1.177, 1.153, 1.178, and 1.162, (b) 1.191, 1.194, 1.153, 1.196, and 1.173, and (c) 1.177, 1.188, 1.163, 1.189, and 1.172. Broken lines calculated by Eq. (10) using data given in Table I.

Scaling exponents for (a) mean square radius of gyration, (b) mean square end-to-end distance, and (c) mean square center-to-end distance as functions of the polymer-solvent parameter . Symbols as in Fig. 1; the gray line is a guide to the eye only.

Scaling exponents for (a) mean square radius of gyration, (b) mean square end-to-end distance, and (c) mean square center-to-end distance as functions of the polymer-solvent parameter . Symbols as in Fig. 1; the gray line is a guide to the eye only.

Ratios of the mean square center-to-end distances and arm length of star-branched chains with arms as a function of the polymer-solvent parameter for constant values of , i.e., (triangles) to (circles).

Ratios of the mean square center-to-end distances and arm length of star-branched chains with arms as a function of the polymer-solvent parameter for constant values of , i.e., (triangles) to (circles).

-values vs number of arms for athermal and theta conditions obtained by DPD (open symbols) compared to results of MC simulations (Ref. 11) (full symbols) in a (a) conventional plot and (b) log-log plot. Circles (triangles) refer to athermal (theta) conditions calculated from prefactors of scaling laws; the dotted line in (a) is calculated by use of Eq. (13); the straight lines in (b) with slopes −0.82 (full line) and −0.64 (broken line) result from linear regression. Results for (near theta conditions) are given in addition (squares).

-values vs number of arms for athermal and theta conditions obtained by DPD (open symbols) compared to results of MC simulations (Ref. 11) (full symbols) in a (a) conventional plot and (b) log-log plot. Circles (triangles) refer to athermal (theta) conditions calculated from prefactors of scaling laws; the dotted line in (a) is calculated by use of Eq. (13); the straight lines in (b) with slopes −0.82 (full line) and −0.64 (broken line) result from linear regression. Results for (near theta conditions) are given in addition (squares).

Shape factors vs polymer-solvent parameter . The value of 1/3 expected for perfectly symmetric coils is indicated by the broken line. MC results are given for comparison (Ref. 11) (full symbols). Types of symbols are as in Fig. 1.

Shape factors vs polymer-solvent parameter . The value of 1/3 expected for perfectly symmetric coils is indicated by the broken line. MC results are given for comparison (Ref. 11) (full symbols). Types of symbols are as in Fig. 1.

Asphericity parameter vs polymer-solvent parameter . MC results are given for comparison (Ref. 11) (full symbols). Types of symbols are as in Fig. 1.

Asphericity parameter vs polymer-solvent parameter . MC results are given for comparison (Ref. 11) (full symbols). Types of symbols are as in Fig. 1.

Diffusion coefficients obtained from mean squared displacements of star-branched chains with arms for (triangles), (circles), and (squares). Straight lines with slopes −0.61, −0.48, and −0.31 result from linear regression.

Diffusion coefficients obtained from mean squared displacements of star-branched chains with arms for (triangles), (circles), and (squares). Straight lines with slopes −0.61, −0.48, and −0.31 result from linear regression.

Log-log plots of the translational diffusion time vs total number of bonds for (open symbols) and (full symbols). Types of symbols are as in Fig. 1.

Log-log plots of the translational diffusion time vs total number of bonds for (open symbols) and (full symbols). Types of symbols are as in Fig. 1.

## Tables

Coefficients and of short-chain correction according to Eq. (10) for mean square dimensions of athermal star-branched chains with arms.

Coefficients and of short-chain correction according to Eq. (10) for mean square dimensions of athermal star-branched chains with arms.

Theta parameters for star-branched chains with arms obtained by the procedures depicted in Fig. 2 and accordingly obtained prefactors of scaling laws of mean square dimensions.

Theta parameters for star-branched chains with arms obtained by the procedures depicted in Fig. 2 and accordingly obtained prefactors of scaling laws of mean square dimensions.

Theta parameters for star-branched chains with arms obtained by the procedures depicted in Fig. 3 and accordingly obtained prefactors of scaling laws of mean square dimensions.

Theta parameters for star-branched chains with arms obtained by the procedures depicted in Fig. 3 and accordingly obtained prefactors of scaling laws of mean square dimensions.

Scaling exponents of the translational diffusion time obtained by DPD and predicted by the Daoud and Cotton model assuming Rouse or Zimm behavior.

Scaling exponents of the translational diffusion time obtained by DPD and predicted by the Daoud and Cotton model assuming Rouse or Zimm behavior.

Article metrics loading...

Full text loading...

Commenting has been disabled for this content