polymers-09-00313.pdf

Polymers

The structural properties of a flexible and semiflexible circular chain confined in an array of parallel nanoposts with a square lattice cross-sectional projection were studied using coarse-grained molecular dynamics simulations. To address the effect of the circular topology, a comparison with linear analogs was also carried out. In the interpretation of the chain structural properties, the geometry of the post array is considered as a combination of a channel approximating the interstitial volume with the diameter d c and a slit approximating the passage aperture with the width w p. The number of interstitial volumes occupied by a chain monotonically increases with the decreasing ratio d c /w p regardless of the way the geometry of the post array is varied. However, depending on how the array geometry is modified, the chain span along the posts displays a monotonic (constant post separation) or a non-monotonic behavior (constant passage width) when plotted as a function of the post diameter. In the case of monotonic trend, the width of interstitial spaces increases with the increasing chain occupation number, while, in the case of non-monotonic trend, the width of interstitial spaces decreases with the increasing chain occupation number. In comparison with linear topology, for circular topology, the stiffness affects more significantly the relative chain extension along the posts and less significantly the occupation number. The geometrical parameters of the post arrays are stored in the single-chain structure factors. The characteristic humps are recognized in the structure factor which ensue from the local increase in the density of segments in the circular chains presented in an interstitial volume or from the correlation of parallel chain fragments separated by a row of posts. Although the orientation correlations provide qualitative information about the chain topology and the character of confinement within a single interstitial volume, information about the array periodicity is missing.

Polymers, 2020, 12(5), 1064, 2020

The conformation and distribution of a flexible and semiflexible chain confined in an array of nanoposts arranged in parallel way in a square-lattice projection of their cross-section was investigated using coarse-grained molecular dynamics simulations. The geometry of the nanopost array was varied at the constant post diameter dp and the ensuing modifications of the chain conformation were compared with the structural behavior of the chain in the series of nanopost arrays with the constant post separation Sp as well as with the constant distance between two adjacent post walls (passage width) wp. The free energy arguments based on an approximation of the array of nanopost to a composite of quasi-channels of diameter dc and quasi-slits of height wp provide semiqualitative explanations for the observed structural behavior of both chains. At constant post separation and passage width, the occupation number displays a monotonic decrease with the increasing geometry ratio dc/wp or volume fraction of posts, while a maximum is observed at constant post diameter. The latter finding is attributed to a relaxed conformation of the chains at small dc/wp ratio, which results from a combination of wide interstitial volumes and wide passage apertures. This maximum is approximately positioned at the same dc/wp value for both flexible and semiflexible chains. The chain expansion from a single interstitial volume into more interstitial volumes also starts at the same value of dc/wp ratio for both chains. The dependence of the axial chain extension on the dc/wp ratio turns out to be controlled by the diameter of the interstitial space and by the number of monomers in the individual interstitial volumes. If these two factors act in the same way on the axial extension of chain fragments in interstitial volumes the monotonic increase of the axial chain extension with the dc/wp in the nanopost arrays is observed. At constant wp, however, these two factors act in opposite way and the axial chain extension plotted against the dc/wp ratio exhibits a maximum. In the case of constant post diameter, the characteristic hump in the single chain structure factor whose position correlates with the post separation is found only in the structure factor of the flexible chain confined in the nanopost array of certain value of Sp. The structure factor of the flexible chain contains more information on the monomer organization and mutual correlations than the structure factor of the semiflexible chain. The stiffer chain confined in the nanopost array is composed of low number of statistical segments important for the presence of respective hierarchical regimes in the structure factor.

The Journal of chemical physics, 2017

Equilibrium conformation of a semiflexible macromolecule in an array of nanoposts exhibits a non-monotonic behavior both at variation of the chain stiffness and increased crowding imposed by nanoposts. This is a result of the competition between the axial chain extension in channel-like interstitial volumes between nanoposts and the chain partitioning among these volumes. The approximation of a nanopost array as a combination of a quasi-channel and a quasi-slit like geometry semi-qualitatively explains the behavior of a chain in the array. In this approximation, the interstitial spaces are viewed as being of the channel geometry, while the passages between two adjacent posts are viewed as being of the slit geometry. Interestingly, the stiffer chains tend to penetrate more readily through the passage apertures, in the direction perpendicular to the post axes, and thus to occupy more interstitial volumes. This is consistent with the prediction of the free-energy penalty that is lower ...

Macromolecules, 2012

The constraints due to the chain closure in combination with the geometrical constraints of a DNA molecule are inevitable for many biological processes. In this work, structural properties of flexible and semiflexible cyclic chains and their linear analogues confined in cylindrical channels were studied using the coarse-grained Metropolis Monte Carlo simulations. The radius of gyration satisfactorily represents the longitudinal stretching of both chain topologies. Transition between the moderate and strong confinement regime of semiflexible cyclic chains is described for the first time. Qualitatively similar response of the chain elongation to the confinement strength variation R g (D) is obtained in the case of cyclic chains. However, the relative chain extension is stronger, the Odijk strong confinement regime is extended to larger channel diameters D, and under moderate confinement the chain extension declines less steeply for cyclic chains. All three findings are explained in terms of the strong self-avoidance of confined chains relative to their linear analogues and the last finding is consistent with the reported experimental measurements. In the Odijk regime, the relative chain extension is governed by the same analytical functions provided half of the contour length for a cyclic chain is considered at the full extension. The orientation correlations for a cyclic chain in narrow channels are characterized by a typical sharp central minimum. Upon increasing the channel cross-sectional area, the minimum is broadened, turns into a negative maximum and, ultimately, the orientation correlations merge with those for a free cycle. Confined flexible and less stiff chains resemble their linear analogues more readily. The static structure factor for tightly confined chains provides better differentiation between the chain architecture than for free chains.

Coarse-grained molecular dynamics simulations of a diblock copolymer consisting of a flexible and semi-flexible block in a dense array of parallel nanoposts with a square lattice packing were performed. The mutual interactions between the two blocks of the confined diblock chain were investigated through a comparison of their size, structure, and penetration among nanoposts with the corresponding separate chains. The geometry of a nanopost array was varied at constant post separation or at constant width of the passage between nanoposts. The size of a single interstitial volume was comparable to or smaller than the size of the diblock chain. A comparison of the blocks with their separate analogous chains revealed that the mutual interactions between the blocks were shielded by the nanoposts and, thus, the blocks behaved independently. At constant passage width, competitive effects of the axial chain extension in interstitial volumes and the lateral chain expansion among interstitial volumes led to a nonmonotonic behavior of the axial span. The position of the maximum in the span plotted against the filling fraction for a diblock chain was dictated by the semi-flexible block. The semi-flexible block penetrates among the nanoposts more readily and the expansion of the whole diblock copolymer is governed by the semiflexible block. The main findings were explained using the free energy arguments when an interstitial volume was approximated by a channel geometry and a passage aperture by a slit geometry. Detail knowledge of controlled conformational behavior in a compartmentalized environment can contribute to new processes in the storage and retrieval of information.

Macromolecular Theory and Simulations, 1999

Using lattice simulations the effect of confinement on the size, orientation and elastic properties of athermal chains was investigated. For chains confined in a slit or in a "cylinder" with square profile a minimum was observed in the dependence of the mean-square end-to-end distance pR 2 P on the plate distance D. However, the components of the mean chain dimensions perpendicular and parallel to the walls, pR 2 k P and pR 2 00 P, steadily diverge with reduction of the pore size. In a slit the distribution functions of the chain vector perpendicular and parallel to the plates, WpR 2 k P and WpR 2 00 P, respectively, were computed. The marked difference between these distribution functions is interpreted as a sign of enhanced alignment of chains of the shape of elongated ellipsoids along the pore walls. A major part of the free energy of confinement DA cf stems from this mechanism of pore-induced macromolecular orientation. A striking anisotropy was observed in the elastic free energies A el k and A el 00 of chains deformed in the direction perpendicular and parallel to the walls and in the corresponding force-displacement functions. Finally, the relation between the elastic free energy A el and the free energy of confinement DA cf and between the forces f and f solv derived thereof is analysed.

2011

Macromolecules, 1994

Effects of intrinsic structural and conformational properties on segmental orientation in uniaxially deformed copolymers are considered. Depedence of segmental orientation on equilibrium values of bond angles, torsional states, and probability distribution of rotameric states is studied. Calculations are carried out for chains with independent as well as pairwise interdependent rotameric states for neighboring bonds using the matrix generation technique of rotational isomeric state formalism. Results invite attention to the importance of specific energy and geometry parameters in prescribing the level of molecular orientation in the two diierent components A and B of AB type copolymers. Results are interpreted with reference to polarized Fourier transform infrared spectroscopy measurements in which the orientation of transition moment vectors is detected. The consequences of certain assumptions in data interpretation such as the choice of cylindrically symmetric reference axes along the chain contour are pointed out. The orientations of vectors along the backbone exhibit strong nonlinear dependence on the conformational characteristics of the component A or B to which they are appended. Thus, the bond vectors of the two monomeric units may exhibit quite distinct orientations, arising only from slight perturbation in bond angles of one of the units. Vectors perpendicular to chain backbone were less sensitive to monomeric structure. Calculations carried out independently by Monte Carlo simulations showed that this method yields an adequate qualitative description of the orientational behavior of chain segments while precise quantitative determination requires the use of the exact matrix generation technique.

Macromolecular Symposia, 2010

The dimensional and structural properties of polymers confined into a cavity are computed by the Monte Carlo method as a function of the chain stiffness. The reduction of the size ratio <R 2 > / < R 2 g > close to 2, distinctive of compact spheres, is observed at squeezing of chains into a capsule. The plots of the static structure factor S(q) computed for stiff chains show characteristic humps attributed to the toroidal structure. The orientation correlation function is found to be a very sensitive indicator of the globule -toroid transition in encapsulated chains. Evidence is presented that the toroidal morphology is formed in stiff polymers when the capsule radius approaches the chain persistence length (D P).

Macromolecules, 1986

A mean-field lattice theory is developed to describe the configurations of long-chain molecules at the crystal/amorphous interface in semicrystalline polymers. Chains are assumed to satisfy continuity and space-filing requirements. The theory permits systematic levels of approximation for correlations among neighboring bonds along the chains subject to the interfacial constraints. We consider the two lowest levels of approximation here: (i) single bonds (two segments) or (ii) bond pairs (three segments). Both models predict that approximately 73% of the chains which emerge from the crystal reenter at sites which are immediately adjacent and that the interfacial region should therefore be small, provided the chains are freely flexible. The models predict that the ratio of chain loop8 to ties in the amorphous region is smaller, and the mean lengths are greater, than predicted by random walk models.