Monte Carlo study of chain conformations in the swollen middle layer of onion‐skin polymeric micelles

Conformations of chains in swollen middle layers of onion‐skin micelles were studied by Monte Carlo simulations on a tetrahedral lattice under conditions that mimic real systems of swollen onion‐skin micelles. Polymer blocks are modeled as tethered self‐avoiding chains, enclosed in a narrow spherical layer. Average density of segments, 〈g_S〉 ca. 0.6, corresponds to swollen micellar systems. Only the excluded volume effect was taken into account since it plays the most important role in dense polymer systems. Individual chains are described by equivalent ellipsoids of gyration. Distributions of the ellipsoid half‐axes were calculated during simulations. Results based on a large series of simulations indicate that the middle layer‐forming blocks may be described as prolonged ellipsoids oriented preferentially perpendicular to the radial direction. Analysis of the data concerning the orientations of end‐to‐end vectors and distributions of segments within one chain indicates that individual chains are strongly interpenetrated and the multi‐chain system is fairly disordered.     

Properties of Star-Branched Polymer Chains Near a Surface

We considered two model systems of star-branched polymers near an impenetrable surface. The model chains were constructed on a simple cubic lattice. Each star polymer consisted of f = 3 arms of equal length and the total number of segments was up to 799. The excluded volume effect was included into these models only and therefore the system was studied at good solvent conditions. In the first model system polymer chain was terminally attached with one arm to the surface. The grafted arm could slide along the surface. In the second system the star-branched chain was adsorbed on the surface and the strength of adsorption was were varied. The simulations were performed using the dynamic Monte Carlo method with local changes of chain conformations. The internal and local structures of a polymer layer were determined. The lateral diffusion and internal mobility of star-branched chains were studied as a function of strength of adsorption and the chain length. The lateral diffusion and internal mobility of star-branched chains were studied as a function of strength of adsorption and the chain length. It was shown that the behavior of grafted and weakly adsorbed chains was similar to that of a free three-dimensional polymer, while the strongly adsorbed chains behave as a two-dimensional system.     

The influence of the polymer chain stiffness on tracer diffusion in polymeric matrices

The diffusion of penetrants in polymers is of technological importance in many areas including chromatography and fuel cell membranes. In this work, the effect of chain conformations on tracer diffusion is studied using molecular simulations and a percolation theory. The polymeric matrix is composed of tangent hard sphere chains that are fixed in space; conformations are changed by tuning the stiffness of the chains. The tracer diffusion coefficient is relatively insensitive to the chain stiffness when polymer chains are frozen as in polymer glasses with the local chain dynamics switched off. An analysis of the matrix using percolation theory shows that the polymer volume fraction at the free volume percolation threshold is also relatively insensitive to the chain stiffness, consistent with the diffusion results. This is surprising because the site‐site intermolecular pair correlation functions in the matrix are quite sensitive to the chain stiffness. In contrast, the tracer diffusion coefficient in a melt of mobile chains decreases significantly as the chain stiffness is increased. We conclude that tracer diffusion is only weakly correlated with the chain conformations and local chain dynamics plays an important role. © 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2011     

Reaction kinetics in dilute solutions of chain molecules carrying randomly spaced reactive and catalytic chain substituents. II. Dependence of the ring closure probability on the solvent medium and the nature of the chain backbone

Ternary copolymers of acrylamide or methacrylamide with small proportions of comonomers carrying reactive p-nitrophenyl ester and catalytic pyridine groups in the side chains were prepared. The kinetics of the ester solvolysis was followed in highly dilute solutions, so that the rate was controlled by interaction of groups carried by the same chain backbone. Data were obtained in water and aqueous methanol and were interpreted by a computer simulation procedure in terms of the dependence of the probability of encounter between two chain substituents on their spacing along the chain backbone. This probability decreased more slowly with increasing separation of the interacting groups when the solvation of the polymer was reduced, but even in solvents approaching θ conditions the results deviated from theoretical predictions for chains without excluded volume. The formation of cyclic conformations is considerably more difficult in methacrylic than in acrylic chains, although the chain flexibility, as characterized by unperturbed chain dimensions, is very similar in the two systems.     

Monte Carlo studies on the deformation behaviour of glassy model systems

We present an alternative methodology for the investigation of deformation properties of polymer glasses. The calculation of the stress–strain relation in simple extension is performed in the framework of a highly flexible lattice Monte Carlo algorithm. In contrast to other studies, this method enables the dynamic and temperature-dependent deformation analysis of an actual multichain system. The most characteristic properties of polymer systems, namely, excluded volume of effective monomers, non-crossability and finite extensibility of the chains as well as van der Waals attraction and the local chain stiffening with decreasing temperature are rigorously accounted for during the dynamics. The simulated stress–strain relations qualitatively agree with experimental findings. Analysis of the structure reveals pronounced non-affine and inhomogeneous deformation behaviour.     

Effects of polymer chain length and stiffness on phase separation dynamics of semidilute polymer solution

Three-dimensional dissipative particle dynamics (DPD) simulations were performed to investigate the phase separation dynamics of semidilute polymer solutions with different polymer chain length and stiffness. For the polymer solution composed of shorter and more flexible chains, a crossover of the domain growth exponent from 1/3 to 2/3 was observed during the course of phase separation, indicating that the growth mechanism altered from diffusion to interfacial-tension driven flow. When the chain flexibility was kept the same but the chain was lengthened to allow for the chain entanglement to occur, the growth exponent changed to 1/4 in the diffusion-dominating coarsening regime while the growth exponent remained 2/3 in the flow-dominating regime. When the chain length was kept short but the stiffness was increased, the growth exponent became 1/6 in the diffusion-dominating regime and little effect was observed in the flow-dominating coarsening regime. The slow down of the phase separation dynamics in the diffusion-dominating coarsening could be explained by that the polymer chains could only perform wormlike movement when chain entanglements occurred or when the chain motion was limited by chain stiffness during phase separation. Moreover, when both the effects of chain length and stiffness were enhanced, polymer networks composed of longer and stiffer chains appeared and imposed an energy barrier for phase separation to occur. As a result, the polymer solution with stiffer and longer chains required a larger quench depth to initiate the phase separation and caused the delay in crossover of the coarsening mechanism from diffusion to flow.     

Motion of a branched polymer chain in confinement: a Monte Carlo study

The aim of the study was a theoretical investigation of the polymer molecules located between two parallel and impenetrable surfaces which were also attractive for polymer segments. The chains were constructed of identical segments and were restricted to knots of a simple cubic lattice. Since the chains were at good solvent conditions the only interactions between the segments of the chain were the excluded volume. The properties of the model chains were determined by means of Monte Carlo simulations with a sampling algorithm based on the chain's local changes of conformation. The differences and similarities in the structure for different adsorption regimes and the size of the slit were shown and discussed. It was observed that at certain conditions the polymer chain was adsorbed at one of the confining surfaces, and then after a certain period of time it detached from this surface and approached the opposite wall; this switch was repeated many times. The influence of the strength of the adsorption, the size of the slit, and the chain's length on the frequency of these jumps were determined. The mechanism of the chain's motion during the switch was also shown.     

Recent developments in asymmetric catalysis using synthetic polymers with main chain chirality

Some recent developments in the use of main chain chiral polymer catalysts are summarized. These polymers are different from the traditional polymer catalysts that are prepared by anchoring monomeric chiral catalysts to an achiral polymer backbone. Three classes of synthetic main chain chiral polymers are discussed including: (1) helical polymers represented by polypeptides; (2) polymers with flexible chiral chains such as polyesters and polyamides; and (3) polymers of rigid and sterically regular chiral chains represented by chiral conjugated polybinaphthyls. Some of these polymer catalysts have shown high enantioselectivity in asymmetric organic transformations.     

高分子线性柔性链在超滤过程中第一类突变现象的观察

利用一种双层结构的膜屏蔽了每个微孔所产生的流场之间的相互作用,从而首次观测到理论上预计的高分子线性柔性链在超滤过程中的第一类突变现象,即仅当宏观流速高于一宏观阈值时,高分子长链方可通过尺寸远小于链无扰半径的微孔,且该宏观阈值与高分子链的长短无关.另外,实验中的过滤膜含有多个微孔,实验结果显示,当一给定的宏观流速低于宏观阈值时,部分微孔会被无法通过的较长的高分子链堵塞,造成未堵塞微孔中的微观流速大于微观阈值.因此,较短的高分子链可从未堵塞的微孔通过滤膜.     

Star-branched polymers in an adsorbing slit: a Monte Carlo study

A coarse-grained model of star-branched polymer chains confined in a slit was studied. The slit was formed by two parallel impenetrable surfaces, which were attractive for polymer beads. The polymer chains were flexible homopolymers built of identical united atoms whose positions in space were restricted to the vertices of a simple cubic lattice. The chains were regular star polymers consisted of f = 3 branches of equal length. The chains were modeled in good solvent conditions and, thus, there were no long-range specific interactions between the polymer beads-only the excluded volume was present. Monte Carlo simulations were carried out using the algorithm based on a chain's local changes of conformation. The influence of the chain length, the distances between the confining surfaces, and the strength of the adsorption on the properties of the star-branched polymers was studied. It was shown that the universal behavior found previously for the dimension of chains was not valid for some dynamic properties. The strongly adsorbed chains can change their position so that they swap between both surfaces with frequency depending on the size of the slit and on the temperature only.     

Monte carlo study of the dynamics of star-branched polymers

A uniform star-branched polymer model with f = 3 arms based on a simple cubic lattice was studied by means of the dynamic Monte Carlo method. The model chain is athermal with excluded-volume interactions and it is flexible. A new type of local micromodification was introduced to make the branching point movable. Static properties of the star polymer are in accordance with other theoretical predictions and experimental evidence. Scaling of the self diffusion constant and the terminal relaxation times is close to those of the Rouse theory and to simulation results of linear chains.     

Monte carlo calculations of second virial coefficients of chain molecules

Monte Carlo calculations have been performed for different types of chain molecules whose units interact through Lennard-Jones potentials. From the averaged Mayer function, we have evaluated the intermolecular two-body cluster integral, obtaining results for second virial coefficients. We have investigated the following points: a) the site modelization of alkanes by comparison of our results with gas phase data of different linear and branched alkanes and their mixtures. b) the prediction of interpenetration factors for flexible linear and star polymer chains in a good solvent (or excluded volume conditions). c) the determination of the theta point for a model of flexible polymer chains and the comparison of data for finite chains with theoretical predictions.     

Lattice model theory of chain stiffening and relaxation properties of macromolecules in the nematic LC state

The relaxation properties of polymer chains In the nematic LC-state or in the external quadrupole field may depend both on the variation of the conformation in the ordered state and on the activation barrier of the molecular (or external) field. This barrier should be surmounted during reorientation of chain elements. The lattice model theory of chain stiffening of macromolecules in the LC-state is proposed. The calculation and comparison of the longitudinal and transversal relaxation spectra for the continuous and discrete rotameric mechanism of the mobility are performed. For the simplest model of a heterogeneous polymer chain the possibility of the more complex relaxational behavior i.e. the existence of two longitudinal and two transversal relaxation spectra was shown.     

Intramolecular phase separation of a copolymer chain with mobile primary structure

The phenomenon of intramolecular phase separation of a single copolymer chain with mobile primary structure (i.e., a polymer chain with reversibly adsorbable ligands) in dilute solution is investigated on the basis of a Flory-type interpolation theory of the coil-globule phase transition. It is shown that under certain critical conditions the stability of the homogeneous primary structure is violated and intramolecular phase separation takes place. Phase diagrams for the cases of rigid and flexible chains are calculated. The main characteristics of a polymer chain in the two-phase state (such as fraction of monomeric units, swelling coefficient and fraction of units with ligands for coexisting intramolecular phases) are investigated.     

A multiple chain Monte Carlo method for atomistic simulation of high molecular weight polymer melts

A new Monte Carlo method is proposed for the simulation of bulk systems of atomistically detailed polymers. Each move consists of a configurational rearrangement of the atoms in a specified region of the material, rather than a specified molecule. Thus atoms within different chains may be displaced cooperatively in each Monte Carlo move. Here, the method is implemented for the case of melts of linear chains, where the bond lengths and bond angles are held constant during the move. The performance of the algorithm is examined for linear polyethylene systems with chain lengths of 100 and 1000 backbone atoms, under a range of conditions. The method shows a considerable potential as a very general and flexible tool for simulating realistic polymer materials, subject to a number of performances limiting factors which are described in detail.     

Integral equation theory for athermal solutions of linear polymers

An integral equation model is developed for athermal solutions of flexible linear polymers with particular reference to good solvent conditions. Results from scaling theory are used in formulating form factors for describing the single chain structure, and the impact of solvent quality on the chain fractal dimension is accounted for. Calculations are performed within the stringlike implementation of the polymer reference interaction site model with blobs (as opposed to complete chains) treated as the constituent structural units for semidilute solutions. Results are presented for the second virial coefficient between polymer coils and the osmotic compressibility as functions of the chain length and polymer volume fraction, respectively. Findings from this model agree with results from scaling theory and experimental measurements, as well as with an earlier investigation in which self-avoiding chains were described using Gaussian form factors with a chain length and concentration-dependent effective statistical segment length. The volume fractions at the threshold for connectedness percolation are evaluated within a coarse-grained closure relation for the connectedness Ornstein-Zernike equation. Results from these calculations are consistent with the usual interpretation of the semidilute crossover concentration for model solutions of both ideal and swollen polymer coils.     

Linear chain surfactants at a planar interface: a comparative Monte Carlo study of several lattice models

Linear chain surfactants in a densely packed arrangement (such as alkane chains in lipid monolayers in the “uniform tilt” structures) are described by a crude coarse-grained model where the endgroups grafted on the interface form a regular lattice and the chains are described by the bond fluctuation model with chains containing N = 4 effective monomers only. Square-well interactions between the monomers are studied for both the attractive and repulsive case for three choices of the interaction range. None of these models exhibits a structure with uniform tilt. For attractive interactions the last bond has a strong tendency to fold back thus leading to a very high density close to the interface. Only when an intrachain-potential favoring stiff chain configurations also is included one can obtain configurations with uniform tilt order. Although related models (with much longer chain lengths and lower grafting densities) are very useful for the study of polymer brushes, the present case of very short chains in a high-density state clearly is plagued by various lattice artefacts and it is concluded that for modelling linear chain surfactants one should use an off-lattice model even on a coarse-grained level.     

Threading-unthreading equilibrium in solution of molecular nanotubes and linear flexible polymer chains

Using the Flory-Huggins lattice model, we investigate the threading-unthreading equilibrium in a solution of linear flexible polymer chains and molecular nanotubes formed by covalently bonding the ringlike molecules, such as cyclodextrins (CDs). It is found that the threading-unthreading equilibrium depends on the temperature and the molar concentrations of the ringlike molecules and polymer chain segments but is independent of the polymer chain length, which agrees with the experimental observations. By fitting the experimental data of alpha-CD and poly(ethylene glycol) (PEG), the inclusion energy between alpha-CD and PEG, which includes the conformation energy loss of PEG resulted from the inclusion, is calculated to be approximately -20.45 kJ/mol per PEG unit.     

Dynamics of grafted star-branched polymers. A Monte Carlo study

Monte Carlo simulations of simple models of star-branched polymers were carried out. The model chains were confined to simple cubic lattice and consisted of f = 3 branches of equal length and the total number of polymer segments as well as the density of grafted chains on the surface were varied. The chains have had one arm end attached to an impenetrable plate. The simulations were performed by employing the set of local micromodifications of the chain conformations. The model chains were athermal, i.e. good solvent conditions were modeled, the excluded volume effect was present at the model. The density of grafted chains on the surface was varied from a single chain up to 0.3. The static and dynamic properties of the system were studied. The influence of polymer concentration as well as the polymer length on static and dynamic properties of the system studied was shown. The relation between the structure and short-time dynamics (relaxation times) was discussed.     

An NMR study of mobility in a crystalline side‐chain comblike polymer

Carbon‐13 spin–lattice relaxation times are measured for poly(octadecyl acrylate) above and below the melting point of the crystalline side chains. The chain backbone has long spin–lattice relaxation times below the melting point that shorten by more than an order of magnitude as the melting point range is traversed. Below the melting point, the backbone is nearly immobilized with spin–lattice relaxation changing very slowly with temperature. Above the melting point, the shorter spin–lattice relaxation times are typical of a rubber above the glass transition and decrease with increasing temperature. The methylene groups in the side chain are quite mobile well below the melting point, indicating fairly rapid anisotropic motion within the crystal. The methyl group at the end of the chain and the adjacent methylene group have longer spin–lattice relaxation times, indicating the greatest side‐chain mobility at the end, which is in the middle of the crystal structure. The side‐chain carbon adjacent to the carbonyl group is as mobile as the majority of the side‐chain carbon, indicating side‐chain mobility extends to all of the side‐chain CH₂ groups. The abrupt transition in the mobility of the backbone is not typical of the amorphous phase in a semicrystalline polymer where the backbone units can crystallize. The close proximity of every backbone segment to the crystalline domain locks backbone segmental motion below the melting point. Melting and crystallization of the side chains switch segmental motion of the backbone on and off. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 1548–1552, 2001