Cylindrically confined self-avoiding chain. In the blob picture, the chain is viewed as a linear string of compression blobs depicted as spheres. Inside each blob of diameter , the effect of wall confinement is considered to be minor; beyond , it tends to align the chain in the longitudinal direction, i.e., along the axis in our convention. For small deformations, the blobs are assumed to be deformed independent of each other, as illustrated by the series of springs in the lower figure.
Equilibrium chain extension (in units of ) of a cylindrically confined self-avoiding chain as a function of the relative confinement . The roman numbers denote the three regimes: the strong confinement (I), intermediate (II), and free chain (III). The diagonal dashed lines in regimes (I) and (II) represent the asymptotic power law ; the dashed line in regime III corresponds to the free chain limit . The data points for up to 300 are MD results, while those for are MC results.
Global relaxation time of the radius of gyration , in units of the relaxation time of a corresponding free chain as a function of the reduced diameter . The solid line marks the asymptotic scaling law of . The inset shows a graph vs , demonstrating for small diameters.
Global relaxation time obtained from the autocorrelation function of , i.e., the longitudinal component of the end-to-end vector. The is given in units of the relaxation time of a corresponding free polymer. Our estimate of increases strongly with decreasing , in contrast to plotted in Fig. 3.
Comparison of two relaxation times: the global relaxation time of the longitudinal component of the radius of gyration, obtained from the autocorrelation function (filled symbols), and that from direct stretch-release simulations (open symbols). The dotted lines are guides to the eyes.
MD results for the distribution of the end-to-end distance for and various pore sizes. The solid lines are Gaussian fits to the graphs.
Ratio of the relaxation time to obtained from MD simulations, as a function of the diameter . As evidenced in the figure, this ratio tends to a -independent constant as decreases.
MD results for the end fluctuation of a confined polymer, rescaled by , as a function of . The peaks are all located at . The solid line represents the scaling expected from the blob approach. In the inset, is rescaled by and the dashed line corresponds to , in accordance with our best fit.
MC results for the end fluctuation of a confined polymer, rescaled by , as a function of . The solid line represents the scaling expected from the blob approach. In the inset, is rescaled by and the dashed line corresponds to , in accordance with our best fit.
MD and MC results for the ratio of the variances of the longitudinal end-to-end distance and the blob size, as a function of the number of blobs . The solid line represents the expected extensiveness . Two types of confined space were used: a cylinder and a brick, i.e., a tube with a circular and a rectangular cross section, respectively.
MD and MC results for the average variance of the single blob size, as a function of the tube diameter . As in Fig. 10, we used two types of confined space, a cylinder and a brick. The solid line represents the theoretically expected scaling.
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