Mean-square Radius Of Gyration Research Articles

Dilute solution properties of poly(di-tert-butyl fumarate)

The mean-square radius of gyration 〈S 2〉 is determined for poly(di-tert-butyl fumarate) (PDtBF) for a range of weight-average number of repeat units n w from 382 to 1520 in tetrahydrofuran at 30.0 °C. The data are analyzed on the basis of the Kratky–Porod (KP) wormlike chain with excluded volume (EV). It is shown that the average chain dimension of PDtBF is significantly larger than that of poly(diisopropyl fumarate) (PDiPF) because of a remarkable difference in chain stiffness between the two polymers.

Molecular dynamics study on polymer filling into nano-cavity by injection molding

Injection molding is one of the cost-effective technologies to produce polymer items towards mass production. In nano-injection molding, the final replication quality of nanostructures is strongly dependent on the filling quality in nano-cavities. In this paper, simulation models for polymer filling into nano-cavities were constructed to investigate the effects of molecular weight and cavity size. The glass transition temperature of isotactic PMMA with different molecular weights was calculated. Characteristics of configuration and snapshots during the filling process were analyzed. Density distribution, velocity profiles and mean-square gyration radius were proposed to investigate the filling quality and the flow behavior. Simulation results showed that the calculated glass transition temperature was higher than the experimental result and increased with the molecular weight. The filling behavior and final replication quality were highly depended on the molecular weight and the cavity size. A higher density distribution was observed in the edges along the nano-cavity by the nonbonding interactions. During the filling process, the gyration radius was firstly decreased rapidly, and then went up to approach the initial value. Atoms in central area exhibited the highest flow velocity, while the velocities of atoms were gradually decreased with the distance from the center.

Phase separation and crystallization in double crystalline symmetric binary polymer blends

Blending of two or more pure polymers is an effective way to produce composites with tunable properties. In this paper, we report dynamic Monte Carlo simulation results on the crystallization of crystalline/crystalline (A/B) symmetric binary polymer blend, wherein the melting temperature of A-polymer is higher than B-polymer. We study the effect of segregation strength (arises from the immiscibility between A- and B-polymers) on crystallization and morphological development. Crystallization of A-polymer precedes the crystallization of B-polymer upon cooling from a homogeneous melt. Simulation results reveal that the morphological development is controlled by the interplay between crystallization driving force (viz., attractive interaction) and de-mixing energy (viz., repulsive interaction between two polymers). With increasing segregation strength, the interface becomes more rigid and restricts the development of crystalline structures. Mean square radius of gyration shows a decreasing trend with increasing segregation strength, reflecting the increased repulsive interaction between A- and B-polymers. As a consequence, a large number of smaller size crystals form with lesser crystallinity. Isothermal crystallization reveals that the transition pathways strongly depend on segregation strength. We also observe a path-dependent crystallization behavior in isothermal crystallization: two-step (sequential) isothermal crystallization yields superior crystalline structure in both A- and B-polymers than one-step (coincident) crystallization.

Universality in Branching Frequencies and Molecular Dimensions during Hyperbranched Polymer Formation: Step Polymerization of AB2 Type Monomer with Equal Reactivity

Hyperbranched polymer formation during step polymerization of AB2 type monomer with equal reactivity of two B's is investigated theoretically, focusing the attention to the degree of branching (DB) and the mean square radius of gyration for the unperturbed chains, . It is found that the DB‐value at large degree of polymerization (P) limit, = 0.5 is unchanged during the whole course of polymerization. The average value of having the same P is invariant throughout the polymerization. The universal curve between and P agrees perfectly with that for the self‐condensing vinyl polymerization (SCVP), another method to synthesize hyperbranched polymers, when the reactivity ratio for SCVP, rSCVP, is 2.589 that gives = 0.5. The power law, is found for large values of P. image

Universality in Branching Frequencies and Molecular Dimensions during Hyperbranched Polymer Formation: 2. Step Polymerization of AB2 Type Monomer with Different Reactivity for the Second B Group

Hyperbranched polymer formation during step polymerization of AB2 type monomer with different reactivity for the second B group is investigated to find the following universal characteristics that are invariant during the whole course of polymerization: (1) The degree of branching (DB) at large degree of polymerization (P) limit, , and (2) the mean square radius of gyration for the unperturbed chains having the same P. The value of and the universal curve for change with the reactivity ratio of two B groups; however, the universal power law holds for large polymers, irrespective of the magnitude of reactivity ratio. The exponent, 0.5, is the same as that for the random branched polymers. Similarities and differences in comparison with random branched polymer formation are discussed. image

Characterization of poly(N,N-diethylacrylamide) and cloud points in its aqueous solutions

The mean-square radius of gyration, second virial coefficient and intrinsic viscosity were determined in methanol at 25.0 °C for two types of poly(N,N-diethylacrylamide) (PDEA) samples that were synthesized by radical polymerization in tert-butanol and benzene using azobis(isobutyronitrile) as an initiator. Analyses of these results indicated that the primary structure of both PDEA samples was linear. The cloud points of the two PDEA samples were also determined in aqueous solutions. For the two types of PDEA samples, the cloud point decreased as the weight-average molecular weight Mw of the sample increased, which is in contrast to previously reported results for poly(N-isopropylacrylamide) (PNIPA) samples, even though those samples have the same hydrophobic chain-end groups. In addition, the cloud-point curve of each PDEA sample has a critical point, which has not been previously reported for PNIPA. The critical point shifted to the upper right with decreasing Mw, as predicted by conventional polymer solution thermodynamics. Therefore, the aqueous PDEA solutions exhibited typical phase behavior that is consistent with the lower critical solution temperature type, which is substantially different from that observed for aqueous PNIPA solutions. The cloud point was determined in aqueous poly(N,N-diethylacrylamide) (PDEA) solutions. It was found that the cloud-point curve of each PDEA sample has a critical point and each PDEA solution exhibits phase separation into two liquid phases when the temperature is increased above its cloud point, which has not been previously observed for aqueous poly(N-isopropylacrylamide) (PNIPA) solutions. Therefore, the aqueous PDEA solutions exhibit typical phase behavior of lower critical solution temperature type, which is substantially different from that observed for PNIPA.

Effect of Stirring Speeds on Microstructure Formation During Thermoplastic Polyurethanes Synthesis

ABSTRACTTwo types of thermoplastic polyurethanes (TPUs) with the same chemical compositions, but with different stirring speeds during the synthesis process, were prepared by a one-step bulk polymerization process. The distinct microstructures of these two samples were characterized in a comprehensive way from primary to tertiary structure. 13C NMR spectra revealed distinctly different characteristics of hard and soft segments' distribution between these two samples. Static light scattering showed the differing mean square radii of gyration and the corresponding secondary structure features. The crystallite features, interface thicknesses, and morphology characteristics of these two samples were studied by differential scanning calorimetry, wide-angle X-ray diffraction, small angle X-ray scattering, and atomic force microscopy. Finally, the mechanism of synthesis was investigated, and a schematic diagram was presented to illustrate the effect of diffusion-controlled phenomena on the propagation of TPUs. Based on the schematic diagram, the formation of distinctly different microstructures due to different stirring speeds could be explained effectively.

Model-Based Reactor Design in Free-Radical Polymerization with Simultaneous Long-Chain Branching and Scission

Polymers are the products of processes and their microstructure can be changed significantly by the reactor systems employed, especially for nonlinear polymers. The Monte Carlo simulation technique, based on the random sampling technique, is used to explore the effect of reactor types on the branched polymer structure, formed through free-radical polymerization with simultaneous long-chain branching and scission, as in the case of low-density polyethylene synthesis. As a simplified model for a tower-type multi-zone reactor, a series of continuous stirred-tank reactors, consisting of one big tank and the same N-1 small tanks is considered theoretically. By simply changing the tank arrangement, various types of branched polymers, from star-like globular structure to a more randomly branched structure, can be obtained, while keeping the following properties of the final products, the monomer conversion to polymer, the average branching and scission densities, and the relationship between the mean-square radius of gyration and molecular weight.

Branched conformational properties of macromolecules in close relation to chemical synthesis. II. Influence of excluded volume interactions.

The description of perturbed particle conformations needs as a prerequisite the algorithm of unperturbed chains which is outlined in Paper I [J. Chem. Phys. 143, 114906 (2015)]. The mean square segment length ⟨r(2)(n)⟩=b(2)n(2ν) with ν = 0.588 for linear chains in a good solvent is used as an approximation also for branched samples. The mean square radius of gyration is easily derived, but for the hydrodynamic, the segment distribution by Domb et al. [Proc. Phys. Soc., London 85, 624 (1965)] is required. Both radii can analytically be expressed by Gamma functions. For the angular dependence of scattered light, the Fourier transform of the Domb distribution for self-avoiding random walk is needed, which cannot be obtained as an analytical function and was derived by numerical integration. The summation over all segment length in the particle was performed with an analytic fit-curve for the Fourier transform and was carried out numerically. Results were derived (i) for uniform and polydisperse linear chains, (ii) or f-functional randomly branched polymers and their monodisperse fractions, (iii) for random A3B2 co-polymers, and (iv) for AB2 hyper-branched samples. The deviation of the Gaussian approximation with the variance of ⟨r(2)(n)⟩=b(2)n(2ν) slightly overestimates the excluded volume interaction but still remains a fairly good approximation for region of qR(g) < 10.

Thermodynamic Properties of a Binary Self-condensing Vinyl Polymerization System in the Presence of Core Initiators†

A self-condensing vinyl polymerization system consisting of B*finitiating cores and AB*inimers was studied by the principle of statistical mechanics. As a result,the internal energy,specific heat,polydispersity index and the mean square radius of gyration of hyperbranched polymers were investigated from viewpoint of thermodynamics. In detail,the effect of some reaction conditions,such as temperature,molar ratio of reactants,volume fraction and the functionality of initiating core,were taken into account. The results show that hyperbranched polymers with expected structures and properties can be prepared by means of optimizing parameters of the reaction condition.

Characterization and Study of Properties in a Polar Solvent of a Functionalized and Quaternized Poly(dimethylsiloxane-co-methyl-hydridosiloxane)

Poly(dimethylsiloxane- co-methyl-hydridosiloxane) (PDMSMHS) with a OSi(CH 3) 2/OSi(HCH 3) molar ratio of 21:1 was functionalized with dimethylallylamine (DMAA) via catalytic hydrosilylation using Karstedt’s catalyst and then quaternized with 1-iodooctane. The functionalized and quaternized co-polysiloxanes (PDMSMHS-1 and PDMSMHS-QAS) were characterized using 1H, 13C and 29Si NMR. The physicochemical properties of the polymeric systems (the differential refractive index increment (dn/dc), the square root of the mean square radius of gyration \(( ^{1/2})\), the average molecular weight (M), and the second virial coefficient (A 2)) were measured in ethanol using gel permeation chromatography/light scattering (GPC/LS). The low percentage (3–4 %) of amino side groups has an unexpected effect on the co-polymers physicochemical properties because the A 2 experimental value for PDMSMHS-1 and PDMSMHS-QAS (8.87×10−3and 1.51×10−2molmLg −2, respectively) indicates that ethanol is a good solvent.

The radius of gyration for a ternary self-condensing vinyl polymerization system

A ternary self-condensing vinyl polymerization (SCVP) system consisting of monomers, inimers and core initiators is studied by the principle of statistical mechanics. Starting from partition functions for polymerization that constructed from two different viewpoints, explicit expressions of the size distribution function (SDF), equilibrium free energy, and the law of mass action are obtained. For two types of hyperbranched polymers (HBPs) formed in the system, the first, the second, and the third mean-square radii of gyration (MSRG) are presented under various conditions. Furthermore, the solvent effect and excluded volume effect are taken into account in the calculation of the MSRG. With these results, the effects of monomers, inimers and core initiators on the spatial dimension of HBPs are discussed. It is shown that the competition between polymers with and without a core in the growing process results in a significant influence on the average properties of the system.

Simulation studies on architecture dependence of unentangled polymer melts.

The dependences of the properties of linear, ring, star, and H-shaped polymer melts on architecture are investigated by nonequilibrium molecular dynamics simulations. We find that zero-shear viscosities η0 for various architectures follow a universal relation, η0=Cη〈Rg0 (2)〉, where Cη is a constant and 〈Rg0 (2)〉 the equilibrium mean-square radius of gyration, in the unentangled regime. This law is also found valid for asymmetrical polymers but invalid for polymers with a hard core, such as stars with many arms and short arm lengths. In the unentangled regime, from the point of view of polymer size, the relaxation times show weak dependences on architecture, but the architecture dependence of the diffusion coefficient is still apparent. Then, we examine unentangled melts of various architectures having the same size over a wide range of shear rates covering linear and nonlinear viscoelastic regimes and find that the rheological quantities, namely, viscosity, first and second normal stress differences, are independent of architecture. In contrast, the polymer deformation shows an apparent dependence on architecture in the nonlinear regime. These findings shall shed significant light on the nature of rheological behaviors of unentangled melts.

Equilibrium and dynamical properties of polymer chains in random medium filled with randomly distributed nano-sized fillers.

The effect of randomly distributed nano-sized fillers on the equilibrium and dynamical properties of linear polymers is studied by using off-lattice Monte Carlo simulation. Lennard-Jones interactions between polymers and fillers are considered. Results show that the statistical dimensions and dynamical diffusion of polymer are dependent on the polymer-filler interaction strength εpf. The mean square radius of gyration 〈RG(2)〉 shows a minimum at a critical polymer-filler interaction εpf*. The value of εpf* decreases with the increase in the polymer length or the concentration of fillers. The exponent ν in 〈RG(2)〉 ∼ N(2ν) is a typical value of self-avoiding walking chain at small εpf but it increases sharply to a bigger value at εpf > εpf*. The mean square displacement decreases with the increase in εpf. Moreover, the normal diffusion of the polymer at weak interactions changes to subnormal diffusion at moderate and strong attractions. We find that polymers diffuse in dilute filler regions at weak attraction and diffuse in dense filler regions at strong attraction.

Size exclusion chromatography of photo-oxidated LDPE by triple detection and its relation to rheological behavior

Sheets of low-density polyethylene (LDPE) were subjected to photo-oxidation in the presence of air using a xenon lamp to irradiate the samples for times between 1 day and 6 weeks. The formation of long-chain branching (LCB) up to one week of degradation and the competition between chain scission and crosslinking at longer periods of radiation were investigated by rheological characterization, Fourier transform infrared spectroscopy, and the solvent extraction method (Rolón-Garrido and Wagner. Polym Degrad Stabil 2014, 99:136, Rolón-Garrido and Wagner. J Rheol 2014, 58:199). In the present contribution the same samples are studied by size exclusion chromatographic characterization using triple detection (concentration, light scattering and viscosity). The gel content is determined by filtration followed by the analysis of the soluble polymer fraction. The influence of photo-oxidation time on the molecular weight distribution (molar masses and polydispersity), the mean square radius of gyration and the intrinsic viscosity contraction factors is discussed. The results are correlated with the model parameters (β and fmax2) of the molecular stress function (MSF) theory, used to describe quantitatively the rheological data in uniaxial elongation. It is verified that LCB occurs as an aside process, which up to one week of degradation dominates over chain scission, before gelation plays a critical role. It is confirmed that the model parameter β correlates with the gel content, which reflects the competition between chain scission and crosslinking, while fmax2 is found to correlate with the experimentally determined contraction factors. By comparing the data of this study with those obtained earlier for polystyrene comb melts with well defined structure, the influence of the branching frequency (i.e. the number of branch points per 1000 carbon atoms) on fmax2 becomes evident.

Structural analysis of telechelic polymer solution using dissipative particle dynamics simulations

A telechelic polymer is an amphiphilic polymer that can form micellar structures when dissolved in water. A telechelic polymer solution shows viscoelastic behaviour owing to the formation of characteristic networks, i.e. loops, bridges and dangling chains. For industrial purposes, telechelic polymers have many applications as thickening agents, such as in paints and cosmetics. Thus, it is desirable to predict and control the rheological properties of telechelic polymers. However, detailed studies at the molecular level have not yet been performed. In this study, I use the dissipative particle dynamics (DPD) method to investigate the relationship between the characteristic structural properties and the molecular structure in telechelic polymer solutions. I show that the morphology of telechelic polymer solutions depends on the concentration and chain length, the distribution of the end-to-end distance, the mean square end-to-end distance, the mean square radius of gyration and the time-averaged mean square displacement. Although an effect of entanglement is important for properties of polymer melts, the polymer chain composed of DPD particles cannot reproduce it. Therefore, I compare telechelic polymer solutions with and without the segmental repulsive potential (SRP), which can simulate the effect of entanglement in DPD simulations. The results indicate that it is necessary to include the SRP in DPD simulations to correctly analyse the behaviour of telechelic polymer solutions.

Structure and dynamics of confined flexible and unentangled polymer melts in highly adsorbing cylindrical pores.

Coarse-grained molecular dynamics simulations are used to probe the dynamic phenomena of polymer melts confined in nanopores. The simulation results show excellent agreement in the values obtained for the normalized coherent single chain dynamic structure factor, S(Q,Δt)/S(Q,0). In the bulk configuration, both simulations and experiments confirm that the polymer chains follow Rouse dynamics. However, under confinement, the Rouse modes are suppressed. The mean-square radius of gyration ⟨R(g)(2)⟩ and the average relative shape anisotropy ⟨κ(2)⟩ of the conformation of the polymer chains indicate a pancake-like conformation near the surface and a bulk-like conformation near the center of the confining cylinder. This was confirmed by direct visualization of the polymer chains. Despite the presence of these different conformations, the average form factor of the confined chains still follows the Debye function which describes linear ideal chains, which is in agreement with small angle neutron scattering experiments (SANS). The experimentally inaccessible mean-square displacement (MSD) of the confined monomers, calculated as a function of radial distance from the pore surface, was obtained in the simulations. The simulations show a gradual increase of the MSD from the adsorbed, but mobile layer, to that similar to the bulk far away from the surface.

Computer simulations of the early stages of crystal nucleation of linear and short chain branched polyethylene on carbon nanotubes

We have used molecular dynamics simulations to study the process of macromolecular organisation of single chain linear and branched polyethylene on the surface of carbon nanotubes. These systems can be considered as good models for the study of the mechanism of polymer folding at the early stage of crystal formation on carbon nanotubes. The mean-squared radius of gyration, the stem length, the bond orientation order parameter and the radial distribution have been used to describe the organisation process and the structure of the chains at the carbon nanotube surface. When compared to the process of organisation of isolated single chains, interesting results are observed: (i) two different mechanisms of chain organisation give rise to different morphologies; lamellar thickening and lateral crystal growth lead to mono- and multilayered structures, independently of the presence of short chain branching; (ii) lamellar thickening is however hindered, but still present, in the case of polymer chains with short chain branches; (iii) both the stem length and the order parameter increase in the nanocomposites with respect to those obtained for isolated chains under the same conditions; (iii) the reorganisation process of thickening is accelerated by the presence of the carbon nanotubes, which act as nucleating agents; and (iv) the presence of short chain branching in polymer chains delays the onset of nucleation and growth of the crystalline structure, suggesting that the process is quite sensitive to the local chain chemistry.

Dilute solution properties of semiflexible star and ring polymers

Our recent theoretical and/or Monte Carlo (MC) studies of dilute solution properties of semiflexible stars and rings are briefly summarized. The theoretical results for the intrinsic viscosity [η] of the Kratky–Porod (KP) wormlike three- and four-arm stars are shown, and effects of chain stiffness on [η] of the stars are examined. A comparison of the results for [η] with those for the effective hydrodynamic radius and the second virial coefficient A2 in a good solvent was made for the semiflexible three-arm stars. It was found that [η] is the most suitable object of study to examine the effects of chain stiffness on average chain dimensions of the stars. As for the rings, the MC results for A2 of the ideal KP rings, which is related to the intermolecular topological interactions, are presented and then compared with the data in the literature for ring atactic polystyrene (a-PS) at Θ for large molecular weight M (1 × 104−6 × 105). Even for ring a-PS in such a range of M, the effects of chain stiffness were still remarkable. The effects of the intramolecular topological constraints on the mean-square radius of gyration and the scattering function of the KP rings are also discussed. Theoretical and/or Monte Carlo studies are made of dilute solution properties of semiflexible stars and rings based on the Kratky–Porod wormlike chain model. The behavior of the properties in the range of the crossover from the rigid limit to the random-coil one is clarified. It is shown that effects of chain stiffness affect largely the dilute solution behavior not only of linear polymers but also of stars and rings, and are still remarkable even for typical flexible polymers with large molecular weight (∼105).

Mean-square radius of gyration and hydrodynamic radius for topological polymers evaluated through the quaternionic algorithm

We evaluate numerically the mean-square (MS) radius of gyration and the diffusion coefficient for topological polymers such as ring, tadpole, double-ring, and caged polymers and catenanes. We consider caged polymers with any given number of subchains, and catenanes consisting of two linked ring polymers with a fixed linking number. Through Kirkwood’s approximation we evaluate the hydrodynamic radius, which is proportional to the inverse of the diffusion coefficient, for various topological polymers. Here we take the statistical averages over configurations of topological polymers constructed through the quaternionic algorithm, which generates uniform random walks connecting given two points. It gives ideal chains with no excluded volume. We evaluate numerically the ratio of the square root of the MS radius of gyration to the hydrodynamic radius for several topological polymers, and show for them that the ratio decreases as the topology becomes more complex.