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Computer simulation of bottle-brush polymers with flexible backbone: Good solvent versus theta solvent conditions
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10.1063/1.3656072
/content/aip/journal/jcp/135/16/10.1063/1.3656072
http://aip.metastore.ingenta.com/content/aip/journal/jcp/135/16/10.1063/1.3656072

Figures

Image of FIG. 1.
FIG. 1.

Plot of ϕ(t) (see Eq. (6)) versus the time t in units of τLJ. Several cases are shown: σ = 0.5, N b = 100, N = 10, T = 3.0 (a); σ = 1.0, N b = 100, N = 20, T = 3.0 (b); and σ = 1.0, N b = 200, N = 40, T = 3.0 (c). The fluctuations of ϕ(t) change sign initially at t ≈ 1500τLJ (a), t ≈ 10000τLJ, and t ≈ 20000τLJ (c) as shown in the inserts.

Image of FIG. 2.
FIG. 2.

Selected snapshot pictures of equilibrated configurations of bottle-brush polymers. Backbone monomers (when visible) are displayed in magenta (darker grey) color, side chain monomers in green (lighter grey). Cases shown refer to σ = 0.5, N b = 100, N = 10, T = 3.0 (a) and T = 4.0 (b), as well as σ = 1.0, N b = 100, N = 20, T = 3.0 (c) and T = 4.0 (d).

Image of FIG. 3.
FIG. 3.

Log-log plot of mean square radius of gyration of the side chains normalized by their chain length and by the square bond length between successive monomers, , versus side chain length N, for σ = 0.5 (a) and σ = 1.0 (b). Data for the bead-spring model at two temperatures (T = 3.0 and T = 4.0), as indicated in the figure are included, as well as three backbone chain lengths (N b = 50, 100, and 200, respectively). For comparison, also data for the athermal bond fluctuation model for comparable backbone chain length are included. Straight lines indicate effective exponents νeff ≈ 0.60 (T = 3.0) or νeff ≈ 0.63 (T = 4.0) in case (a), and νeff ≈ 0.60 (T = 3.0) or νeff ≈ 0.64 (T = 4.0) in case (b). For the bond fluctuation model under very good solvent conditions the slightly larger effective exponent (νeff ≈ 0.65 for σ = 0.5, and νeff ≈ 0.66 for σ = 1.0) than for the off-lattice model with T = 4.0 results.

Image of FIG. 4.
FIG. 4.

Temperature dependence of the normalized mean square radius of gyration for four chain lengths (N = 5, 10, 20, and 40), and three backbone lengths (N b = 50, 100, and 200), respectively. All data are for the bead-spring model and σ = 1. Data for bottle-brush polymers with flexible backbone are connected by curves to guide the reader's eyes. Data are only shown for T = 3.0 and 4.0 for the rigid backbone case.

Image of FIG. 5.
FIG. 5.

Log-log plot of versus side chain length N, for the bond fluctuation model with σ = 0.5 (a) and σ = 1.0 (b) including different choices of N b as indicated.

Image of FIG. 6.
FIG. 6.

Plot of the effective exponent ζ, extracted from the slope of the straight lines in Fig. 5, versus the backbone chain length N b for σ = 0.5 (a) and σ = 1.0. All data are for the athermal bond fluctuation model.

Image of FIG. 7.
FIG. 7.

Log-log plot of versus N. All data are for the bead-spring model with σ = 1.0 at both T = 4.0 (a) and T = 3.0 (b). Three backbone lengths are shown as indicated.

Image of FIG. 8.
FIG. 8.

Log-log plot of versus backbone chain length N b , for σ = 0.5 (a) (b) and σ = 1.0 (c) (d), including both T = 3.0 (a) (c) and T = 4.0 (b) (d), for the bead-spring model. Several side chain lengths N are included as indicated. Straight lines indicate a fit with effective exponents νeff.

Image of FIG. 9.
FIG. 9.

Log-log plot of for the bond fluctuation model versus backbone chain length N b , for 67 ⩽ N b ⩽ 259, and several side chain lengths N, for σ = 0.5 (a) and σ = 1.0 (b). Part (c) shows the plot of rescaled radius of gyration of the bottle-brush polymers versus N b for σ = 1.0. The persistence length l p, Rg is determined by the values of plateau. Part (d) shows a crossover scaling plot, collapsing for N = 6, 12, 18, and 24, σ = 1.0, and all data for 67 ⩽ N b ⩽ 1027 on a master curve, that describes the crossover from rods to swollen coils . For this purpose, N b is rescaled with the blob diameter s blob, which has been determined to be s blob = 6, 10, 12, and 14 for N = 6, 12, 18, and 24, respectively.6,11

Image of FIG. 10.
FIG. 10.

Semi-log plot of 〈cos θ(s)〉 vs. s for the bead-spring model with σ = 0.5. Data are chosen for N b = 50 (a) (b) and N b = 200 (c) (d) at T = 3.0 (a) (c) and T = 4.0 (b) (d), respectively. Several choices of N are shown as indicated. Straight lines illustrate fits to a exp (− bs), with constants a, b quoted in the figure.

Image of FIG. 11.
FIG. 11.

Semi-log plot of 〈cos θ(s)〉 vs. s for the bead-spring model with σ = 1.0 and N b = 100 at the temperatures T = 3.0 (a) and T = 4.0 (b), respectively. Several choices of N are shown as indicated. Straight lines illustrate fits to a exp (− bs), with constants a, b as quoted in the figure.

Image of FIG. 12.
FIG. 12.

Log-log plot of the effective persistence length as a function of side chain length N for T = 3.0 (a) (c) and T = 4.0 (b) (d) for several choices of N b . Results for σ = 1.0 and σ = 0.5 are shown as indicated and the exponent estimates ζ extracted from the slope are listed. Values of are also listed in Table I.

Image of FIG. 13.
FIG. 13.

Plot of the function νeff(L/l p ) versus L/l p as predicted from the Kratky-Porod model, Eqs. (16) and (17) (full curves). The numbers for L/l p extracted for σ = 0.5 (a) and σ = 1.0 (b) are quoted in the figure for various N at the abscissa. The average of the exponents νeff from Figs. 8(a) and 8(c) and from (not shown) are quoted on the ordinate. Log-log plot of vs. L/l p (N) for σ = 0.5 (c) and σ = 1.0 (d). Several choices of N are shown as indicated. Data plotted by the same symbol correspond to N b = 50, 100, and 200 from left to right. The prediction for the Kratky-Porod model (Eq. (16)) is also shown for comparison. Approximate data collapse are obtained by introducing a factor of a r (a r = 9.2 ± 1.4. and 4.9 ± 0.2 for σ = 0.5 and 1.0, respectively), cf. text. Values of l p (N) are also listed in Table I.

Tables

Generic image for table
Table I.

Estimates of the effective persistence length shown in Fig. 12 are listed for the BS model with the grafting densities σ = 0.5 and 1.0 at temperatures T = 3.0 and 4.0. Various values of the backbone length N b and the side chain length N are chosen here. All length quoted in this table are given in units of ℓ b (with ℓ b ≈ 0.97σLJ). Note that depends not only on N and σ, but also on N b and T, and hence does not seem as a characteristic of intrinsic chain stiffness. Estimates of l p (N) shown in Fig. 13 are also listed for comparison.

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/content/aip/journal/jcp/135/16/10.1063/1.3656072
2011-10-31
2014-04-16
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Computer simulation of bottle-brush polymers with flexible backbone: Good solvent versus theta solvent conditions
http://aip.metastore.ingenta.com/content/aip/journal/jcp/135/16/10.1063/1.3656072
10.1063/1.3656072
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