1887
banner image
No data available.
Please log in to see this content.
You have no subscription access to this content.
No metrics data to plot.
The attempt to load metrics for this article has failed.
The attempt to plot a graph for these metrics has failed.
Effect of hydrodynamic correlations on the dynamics of polymers in dilute solution
Rent:
Rent this article for
USD
10.1063/1.4799877
/content/aip/journal/jcp/138/14/10.1063/1.4799877
http://aip.metastore.ingenta.com/content/aip/journal/jcp/138/14/10.1063/1.4799877

Figures

Image of FIG. 1.
FIG. 1.

Analytical center-of-mass velocity correlation functions . (a) Transverse [Eq. (36) ] (solid lines) and magnitudes of longitudinal [Eq. (41) ] (dashed lines) correlation functions. The dashed-dotted lines represent negative parts. (b) Total correlation functions (solid lines) and the contributions of the transverse parts (dashed lines). The magenta line indicates the fluid long-time tail according to Eq. (38) . The polymer lengths are L p /l = 10, 102, 103, 104, and 105 (top to bottom).

Image of FIG. 2.
FIG. 2.

Analytical longitudinal center-of-mass velocity correlation functions for the polymer lengths L p /l = 10, 103, and 105 (top to bottom). The solid lines represent the full expression (41) and the dashed lines the approximation (44) .

Image of FIG. 3.
FIG. 3.

Analytical center-of-mass velocity correlation functions of the polymer of length L p /l = 103 and the collision time steps (red), 0.01 (blue), 0.03 (green), and 0.1 (black). These values correspond to the kinematic viscosities , 8.2, 2.8, and 0.9.

Image of FIG. 4.
FIG. 4.

Polymer center-of-mass velocity autocorrelation functions. (a) The polymer length is N m = 160 and the collision time step ( ). The inset shows the data in semilogarithmic representation. (b) The polymer length is N m = 80 and ( ). The negative parts of C v are shown by dashed lines. The simulation results are displayed by red lines, the analytical results (33) by black lines, and the transverse contributions by green lines. The blue line in (a) indicates the correlation function of MPC particles. 65 The maximum mode numbers are (a) n m = 33 and (b) n m = 25 [cf. Eq. (60) ].

Image of FIG. 5.
FIG. 5.

(a) Simulation results for polymer center-of-mass velocity autocorrelation functions of Gaussian polymers of lengths N m = 40, 80, 160, 320, 640, and 1280 (top to bottom), and (b) self-avoiding polymers of lengths N m = 40, 80, 160, 320, and 640 (top to bottom). The black lines correspond to the analytical approximation (33) with the maximum mode numbers (a) n m = 15, 25, 33, 50, and 40 for the two longer polymers, and (b) n m = 27, 43, 57, and 50 for the longer ones, respectively. The straight lines indicate the long-time tail, and the magenta lines, for the longest polymers, the correlation functions for infinite systems.

Image of FIG. 6.
FIG. 6.

Time integrals of the center-of-mass velocity autocorrelation functions (61) of Gaussian polymers of length N m = 80 for the collision time steps step (blue), 0.05 (green), 0.02 (red), and 0.004 (black) (bottom to top). The corresponding kinematic viscosities are , 1.67, 4.12, and 20.54, respectively. The product μD(t) is scaled by the kinematic viscosity and the diffusion coefficient for the collision time step .

Image of FIG. 7.
FIG. 7.

(a) Center-of-mass velocity correlation functions of polymers of length N m = 80. The lengths of the simulation boxes are L/a = 40 (green) and 140 (blue). At short times the two correlations are indistinguishable. The black and light blue lines are the corresponding theoretical results. The dashed line is the infinite system limit. (b) Integrated correlation functions. The same color code is applied as in (a). The black line follows as integral over the correlation function of the simulations up to and the theoretical correlation C v (t) beyond that time. The asymptotic value of the diffusion coefficient of the infinite system is .

Image of FIG. 8.
FIG. 8.

(a) Means quare displacements of monomers (solid lines) and of polymer centers-of-mass (dashed-dotted lines) for Gaussian polymers. (b) Monomer MSDs in the center-of-mass reference frame . (c) Local slopes [Eq. (66) ] of the MSDs of (a) and (b): ζ m (t) (squares), ζ cm (diamonds), and ζ t (bullets). The polymer lengths are N m = 80 (red), 160 (blue), 320 (purple), 640 (light-blue), 1280 (with ) (orange), and 1280 (with ) (black). The dark-green curves are theoretical results following from Eqs. (50)–(52) . Inset in (b): Polymer-length dependence of the relaxation times. The solid line shows the power-law .

Image of FIG. 9.
FIG. 9.

(a) Mean square displacements of self-avoiding polymers: Monomer MSDs in the center-of-mass reference frame (solid lines), total monomer MSDs (dashed lines), and center-of mass MSDs (dashed-dotted lines). The polymer lengths are N m = 40 (green), 80 (red), 160 (blue), 320 (purple), and 640 (light-blue). The dark-green curves are theoretical results following from Eqs. (50)–(52) . (Inset) Polymer-length dependence of the relaxation times. The solid line shows the power-law , with ν = 0.6. (b) Local slopes [Eq. (66) ] of the MSDs of (a): ζ m (t) (squares), ζ cm (diamonds), and ζ t (bullets).

Tables

Generic image for table
Table I.

Simulation parameters and results for Gaussian phantom chains. N m denotes the number of monomers, L is the length of the simulation box, R g is the radius of gyration, and τ r is the end-to-end vector relaxation time.

Generic image for table
Table II.

Simulation parameters and results for self-avoiding polymers. N m denotes the number of monomers, L is the length of the simulation box, R g is the radius of gyration, and τ r is the end-to-end vector relaxation time.

Loading

Article metrics loading...

/content/aip/journal/jcp/138/14/10.1063/1.4799877
2013-04-11
2014-04-24
Loading

Full text loading...

This is a required field
Please enter a valid email address
752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Effect of hydrodynamic correlations on the dynamics of polymers in dilute solution
http://aip.metastore.ingenta.com/content/aip/journal/jcp/138/14/10.1063/1.4799877
10.1063/1.4799877
SEARCH_EXPAND_ITEM