Peter Cifra

3D entrapment of polymers in nanocavities is crucial for a variety of synthetic and biomimetic materials, including hollow particles. We evaluate the effect of chain stiffness on the properties of polymers entrapped in cavities/capsules using molecular simulation. Two confinement‐induced phenomena are found to control the polymer distribution ρ ( r ) across the closed sphere. The near‐wall entropic depletion, characteristic of flexible polymers, manifests itself in monotonous profiles similar to those around a solid sphere in open systems. Contrarily, in moderately stiff polymers, the confining surface generates distinct density enrichment in profiles due to the development of toroidal conformations. The energetics of toroidal growth in a semidilute solution is quantified by simulation. The computed bending energy confirms a simpler generation of toroids in short polymers. The observed reduction of the persistence length in a cavity facilitates the growth of toroids. The thickness of the depletion layer determined by the novel universal method is in agreement with the data from the restricted conventional method. A close relationship is demonstrated between the concentration changes in the depletion thickness and the radius of gyration. The relevance of the computed confinement effects to bioanalytical or biomedical applications of capsules/hollow particles is discussed.

Nanoscale confinement of polymers in a cavity is central to a variety of biological and nanotechnology processes. Using the discrete WLC model we simulate the compression of flexible and semiflexible polymers of linear and ring topology in a closed cavity. Simulation reveals that polymer pressure inside the cavity increases with the chain stiffness but is practically unaffected by the chain topology. For flexible polymers, the computed dependence of pressure on the cavity size and polymer concentration is consistent with the scaling behavior expected for bulk polymers in a good solvent. However, the scaling behavior of semiflexible polymers is only in partial agreement with the theory prediction, with discrepancies arising from a continuous transition between regimes in chains of moderate lengths. The computed segment density profiles endorse the propensity of semiflexible polymers to concentrate beneath the cavity surface and thus elevate the pressure. The compaction of polymers by compression into the disordered globule or growing toroidal structure is documented.

We compute by molecular simulation the energy/entropic partition of the force in a stretched double‐stranded (ds)DNA molecule that is not yet available from the single‐molecule measurements. Simulation using the coarse‐grained wormlike chain (WLC) model predicts a gradual decrease in the internal (bending) energy of DNA at stretching. The ensuing negative energy contribution to force f_U is outweighed by the positive entropy contribution f_S. The ratio f_U/f, used to assess the polymer elasticity, is about −1 at the moderate extension of DNA. At the high extension, the extra energy expenses due to the contour length elongation make the ratio f_U/f less negative. The simulation findings of the hybrid energy/entropy nature of DNA elasticity at weak and moderate forces are supported by computations using the thermoelastic method mimicking the polymer experiments in bulk. It is contended that the observation of the negative energy elasticity in DNA can be generalized to other semiflexible polymers described by the WLC model.

Molecular simulations in nanochannels are used to explore the compression elasticity of ring polymers of stiffness (persistence length) similar to DNA. By combination with the parallel data for linear polymers, the effect of chain topology on their compression behavior is assessed. The results show that the ring polymers are much less bendable at longitudinal compression than the linear analogs. The chain span of linear polymers is continuously reduced at compression, whereas in ring polymers, an abrupt decrease of the span is observed. The simulation data elucidate this phenomenon as the buckling of a ring polymer into the double‐folded hairpin. The shrinking ratio of sizes of the ring and linear chains shows a complex behavior much differing from the existing reports. The force–displacement functions for chains of both topologies at moderate confinement are very well accounted for by the mean‐field Flory scheme. The theory predicts the difference in the mechanical stiffness of the ring and linear polymers in qualitative agreement with the simulation data. These findings are relevant to the compression behavior of semiflexible ring polymers under spatial constraints such as in nanofluidic experiments, disordered media, or cellular environment.

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 d_p 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 S_p as well as with the constant distance between two adjacent post walls (passage width) w_p. The free energy arguments based on an approximation of the array of nanopost to a composite of quasi-channels of diameter d_c and quasi-slits of height w_p 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 d_c/w_p 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 d_c/w_p ratio, which results from a combination of wide interstitial volumes and wide passage apertures. This maximum is approximately positioned at the same d_c/w_p 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 d_c/w_p ratio for both chains. The dependence of the axial chain extension on the d_c/w_p 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 d_c/w_p in the nanopost arrays is observed. At constant w_p, however, these two factors act in opposite way and the axial chain extension plotted against the d_c/w_p 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 S_p. 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.

We study the compression and extension response of single dsDNA molecules confined in cylindrical channels by means of Monte Carlo simulations. The elastic response of µm-sized DNA to the external force acting through the chain ends or through the piston is markedly affected by the size of the channel. The interpretation of the force (f)-displacement (R) functions under quasi-one-dimensional confinement is facilitated by resolving the overall change of displacement ΔR into the confinement contribution ΔRD and the force contribution ΔRf. The external stretching of confined DNA results in a characteristic pattern of f-R functions involving their shift to the larger extensions due to the channel-induced pre-stretching ΔRD. A smooth end-chain compression into loop-like conformations observed in moderately confined DNA can be accounted for by the relationship valid for a Gaussian chain in bulk. In narrow channels, the considerably pre-stretched DNA molecules abruptly buckle on compression by the backfolding into hairpins. On the contrary, the piston compression of DNA is characterized by a gradual reduction of the chain span S and by smooth f-S functions in the whole spatial range from the 3d near to 1d limits. The observed discrepancy between the shape of the f-R and f-S functions from two compression methods can be important for designing nanopiston experiments of compaction and knotting of single DNA in nanochannels.

The elasticity of dsDNA molecules is investigated by Monte Carlo simulations based on a coarse-grained model of DNA. The force-displacement (f-r) curves are computed under the constraints of the constant force (Gibbs) or the constant length (Helmholtz) ensemble. Particular attention was paid to the compressional (negative) and weak tensile forces. It was confirmed that simulations using the vector Gibbs ensemble fail to represent the compression behavior of polymers. Simulations using the scalar Gibbs protocol resulted in a qualitatively correct compressional response of DNA provided that the quadratic averages of displacements were employed. Furthermore, a well-known shortcoming of the popular Marko-Siggia relation for DNA elasticity at weak tensile forces is elucidated. Conversely, the function f-r from the simulation at the constant length constraint, as well as the new closed-form expressions, provides a realistic depiction of the DNA elasticity over the wide range of negative and positive forces. Merely a qualitative resemblance of the compression functions f-r predicted by the employed approaches supports the notion that the elastic response of DNA molecules may be greatly affected by the specifics of the experimental setups and the kind of averaging of the measured variable.

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.