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Equilibrium partitioning of macromolecules in confining geometries: Improved universality with a new molecular size parameter
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10.1063/1.2842073
/content/aip/journal/jcp/128/12/10.1063/1.2842073
http://aip.metastore.ingenta.com/content/aip/journal/jcp/128/12/10.1063/1.2842073

Figures

Image of FIG. 1.
FIG. 1.

A polymer chain of given configuration is confined in a slit of width and orientation . This problem is essentially one dimensional (1D). By projecting the polymer configuration onto , we obtain as the maximum covered distance in direction. In order for this configuration not to be intersected by the slit walls, the first bead can only be located in the region in the direction. The probability that this configuration is not intersected by the slit walls is .

Image of FIG. 2.
FIG. 2.

Example of a 3D structure for a flexible linear RW polymer and its coarse-grained model: An elastic dumbbell.

Image of FIG. 3.
FIG. 3.

Characteristic ratios , , and obtained from linear RW and SAW simulations are plotted as a function of the total number of beads, . Solid lines are predictions based on Eqs. (48)–(50).

Image of FIG. 4.
FIG. 4.

Distribution functions of are shown for a rigid rod, an elastic dumbbell, and a linear RW polymer of beads. Points are our simulations results, and solid lines are predictions based on Eqs. (32), (35), and (43).

Image of FIG. 5.
FIG. 5.

Equilibrium partition coefficients as a function of are shown for a long chain linear RW polymer with (from top to bottom) a slit of width , a long square channel of cross section, a long cylinder of diameter , a cubic box of size , and a sphere of diameter . Both our simulation results and analytical results given in Eqs. (41) and (51) are shown for slit, square channel, and cubic box confining geometries, and they nearly coincide with one another even for as small as . For cylinder and sphere confining geometries, only Casassas results are shown (Ref. 1).

Image of FIG. 6.
FIG. 6.

Equilibrium partition coefficients as a function of are shown for linear RW polymers of beads with a slit confining geometry of width . From top to bottom: , and . The analytical solution for a rigid dumbbell (Ref. 14) is also plotted, which coincides with the simulation results of . Casassa’s result (Ref. 1) given by Eq. (41) corresponds to .

Image of FIG. 7.
FIG. 7.

Equilibrium partition coefficients as a function of are shown for linear SAW polymers of beads with a slit confining geometry of width . From top to bottom: , simulation results of a linear RW chain of , and Casassa’s result (Ref. 1) given by Eq. (41) corresponding to a linear RW chain of .

Image of FIG. 8.
FIG. 8.

Equilibrium partition coefficients as a function of are shown for linear RW polymers of beads with a slit confining geometry of width . From top to bottom: , and . Casassa’s result (Ref. 1) given by Eq. (41) corresponds to , which nearly coincides with the simulation results for .

Image of FIG. 9.
FIG. 9.

Equilibrium partition coefficients as a function of are shown for linear SAW polymers of beads with a slit confining geometry of width . From top to bottom: , simulation results of a linear RW chain of , and Casassa’s result (Ref. 1) given by Eq. (41) corresponding to a linear RW chain of .

Image of FIG. 10.
FIG. 10.

Equilibrium partition coefficients are shown (a) as a function of , (b) as a function of , (c) as a function of , and (d) as a function of for (from top to bottom) a linear SAW polymer of , a linear RW polymer of , a symmetric three-arm RW star polymer of arm length with , and a symmetric four-arm RW star polymer of arm length with with a slit confining geometry of width . In subfigure (d), are also shown for an elastic dumbbell, a rigid rod, and a sphere.

Image of FIG. 11.
FIG. 11.

Equilibrium partition coefficients are shown (a) as a function of , (b) as a function of , (c) as a function of , and (d) as a function of for (from top to bottom) a linear SAW polymer of , a linear RW polymer of , a symmetric three-arm RW star polymer of arm length , and a symmetric four-arm RW star polymer of arm length with a square channel confining geometry of cross section. In subfigure (d), for a sphere is also shown.

Image of FIG. 12.
FIG. 12.

Equilibrium partition coefficients are shown (a) as a function of , (b) as a function of , (c) as a function of , and (d) as a function of for (from top to bottom) a linear SAW polymer of , a linear RW polymer of , a symmetric three-arm RW star polymer of arm length , and a symmetric four-arm RW star polymer of arm length with a cubic box confining geometry of size . In subfigure (d), for a sphere is also shown.

Tables

Generic image for table
Table I.

The steric exclusion radius and root-mean-square radius of gyration for some simple rigid objects: A uniform sphere (sphere) and a spherical shell (shell) both of radius ; a thin rod (rod) and a rigid dumbbell (dumbbell) both of length ; a uniform thin disk (disk) and a rigid ring (ring) both of radius .

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/content/aip/journal/jcp/128/12/10.1063/1.2842073
2008-03-27
2014-04-20
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Equilibrium partitioning of macromolecules in confining geometries: Improved universality with a new molecular size parameter
http://aip.metastore.ingenta.com/content/aip/journal/jcp/128/12/10.1063/1.2842073
10.1063/1.2842073
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