Regular Star Polymers Research Articles

Supramolecular Synthesis of Star Polymers.

Supramolecular polymers, in which monomers are assembled via intermolecular interactions, have been extensively studied. The fusion of supramolecular polymers with conventional polymers has attracted the attention of many researchers. In this review article, the recent progress in the construction of supramolecular star polymers, including regular star polymers and miktoarm star polymers, is discussed. The initial sections briefly provide an overview of the conventional classification and synthesis methods for star polymers. Coordination-driven self-assembly was investigated for the supramolecular synthesis of star polymers. Star polymers with multiple polymer chains radiating from metal-organic polyhedra (MOPs) have also been described. Particular focus has been placed on the synthesis of star polymers featuring supramolecular cores formed through hydrogen-bonding-directed self-assembly. After describing the synthesis of star polymers based on host-guest complexes, the construction of miktoarm star polymers based on the molecular recognition of coordination capsules is detailed.

AF4/MALS/QELS/DRI characterization of regular star polymers and their "span analogs".

Asymmetric flow field-flow fractionation (AF4) coupled with multi-angle static and quasi-elastic light scattering and differential refractive index detectors, was employed for the separation and characterization of regular star-shaped polystyrenes and their linear and span analogs in tetrahydrofuran. Stars with different arm lengths were separated from each other by employing a binary slope cross-flow gradient. Cross-flow optimization enabled fast separation of polystyrenes in two- and three-component blends. Macromolecular parameters were obtained by using light-scattering and refractive index detection, and properties of polystyrenes with different molecular architectures were compared. To our knowledge, this is the first report on the separation of star polymers by AF4. Novel characterization approaches for stars are important from both applied and fundamental standpoints, as these macromolecules are valued for their tribological, drug delivery, catalytic and coating capabilities, and also serve as model compounds for the structured study of long-chain branching and its effects in polymers.

A Monte Carlo Study of the Second Virial Coefficient of Semiflexible Regular Three-Arm Star Polymers

A Monte Carlo (MC) study is made of the second virial coefficient A2 along with the mean-square radius of gyration for regular three-arm star and linear freely rotating chains of bond angles θ ranging from 109° (typical flexible chain) to 175° (typical semiflexible or stiff chain) with the Lennard–Jones 6-12 potentials between beads corresponding to a good solvent system, in the range of the total number n of bonds from 30 to 900. On the basis of the MC values of A2 so obtained, an examination is made of effects of chain stiffness on the ratio of A2 of the star chain to that of the linear one, both chains having the same n and θ. It is then found that is rather insensitive to change in θ (chain stiffness) in contrast to the cases of the ratios gS and gη related to and the intrinsic viscosity [η], respectively, which remarkably decrease with increasing θ.

A Monte Carlo Study of the Intrinsic Viscosity of Semiflexible Regular Three-Arm Star Polymers

A Monte Carlo (MC) study is made of the intrinsic viscosity [η] and also of the mean-square radius of gyration <S2> for regular three-arm star freely rotating chains of bond angles θ=109°, 165°, and 175° and with the Lennard–Jones 6-12 potentials between beads having the parameter values corresponding to the Θ temperature, in the range of the total number n of bonds in the chain from 60 to 300. Three kinds of approximate values of [η] are calculated by the use of the Kirkwood–Riseman (KR) approximation, the Zimm rigid-body ensemble approximation which gives an upper bound [η](U) to [η], and by the Fixman method which gives a lower bound [η](L), the KR value of [η] being designated [η](KR). On the basis of the three kinds of MC values of [η] so obtained, the behavior of the ratio gη of [η] for the star chain to that for the linear one, both having the same n, is examined as a function of the reduced contour length λL as defined as the total contour length L of the corresponding Kratky–Porod (KP) wormlike chain divided by its stiffness parameter λ−1, the values of λL having been determined from an analysis of the present and previous MC data for <S2> on the basis of the KP chain. It is found that the KR value gη(KR) of gη as defined by [η](KR)(star)/[η](KR)(linear) lies between the values of an upper bound gη(U) and a lower one gη(L), which are defined by [η](U)(star)/[η](L)(linear) and [η](L)(star)/[η](U)(linear), respectively, irrespective of the values of λL. Further, the difference between the two bounds becomes very small for small λL, indicating that gη(KR) may give a good approximate value for semiflexible or stiff chains.

Polymer-like to Soft Colloid-like Behavior of Regular Star Polymers Adsorbed on Surfaces

We investigated systematically the structure and growth of monolayers of physisorbed polybutadiene (PB) starlike polymers on freshly cleaved mica after solvent evaporation using atomic force microscopy (AFM). We observed a strong dependence of the evolution of the average island height and surface coverage with increasing surface density on the functionality (number of arms) of the star polymers. We explain these structural phenomena in terms of the molecular and conformational properties of the different star polymers. Our study provides real space observations of the star polymer surface structures near the overlap surface density for the first time. The structural regimes are strongly affected by the change of the star polymer behavior from polymer-like to colloid-like when the arm functionality increases.

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.

Starlike Micelles with Starlike Interactions: A Quantitative Evaluation of Structure Factors and Phase Diagram

Starlike PEP-PEO block copolymer micelles offer the possibility to investigate the phase behavior and interactions of regular star polymers (ultrasoft colloids). Micellar functionality f can be smoothly varied by changing solvent composition (interfacial tension). Structure factors obtained by small-angle neutron-scattering can be quantitatively described in terms of an effective potential for star polymers. The experimental phase diagram reproduces to a high level of accuracy the predicted liquid-solid transition. Whereas for intermediate f a bcc phase is observed, for high f the formation of a fcc phase is preempted by glass formation.

Precise Synthesis of Regular and Asymmetric Star Polymers and Densely Branched Polymers with Starlike Structures by Means of Living Anionic Polymerization

The subject of this review is to present new synthetic methodologies recently developed by us, which are applicable to both regular and asymmetric star polymers with well-defined architectures. The first methodology involves the coupling reaction of a variety of living anionic polymers of styrene, α-methylstyrene, isoprene, tert-butyl methacrylate, and ethylene oxide with novel chain-end- and in-chain-functionalized polymers with a definite number of benzyl halide moieties intentionally designed as polymeric coupling agents. In the second methodology, we propose a new concept based on iterative approach, with which star polymers can be successively and, in principle, unlimitedly synthesized by repeating the iterative reaction sequence. Finally, a convenient synthesis of densely branched polymers with starlike structures is presented by the quantitative coupling reaction of living anionic polymers with reactive benzyl halide-functionalized backbone polymers based on a grafting-onto method.

Stress Relaxation of Multi-Arm Star Polystyrenes in the Molten State.

Stress relaxation of multi-arm star polystyrenes were investigated in the molten state. The relaxation modulus was measured over a wide range of strain. The plots of relaxation modulus against time for the multi-arm stars showed a new mechanical relaxation at long times. For entangled systems, although the strain dependence of the damping function for entanglement relaxation was almost identical to that for linear and regular star polymers, the strain dependence for the long-time relaxation was weak. On the other hand, the damping function for the non-entangled systems showed the stronger dependence than the entangled systems. The damping at large strains became weaker with increasing weight-average molecular weight of the arm but appeared to be independent of number of arms.

Effects of Substrate Interactions in Liquid Chromatography of Star Homopolymers and Star Block Copolymers

A theoretical study of the behavior in liquid chromatography of star polymers of two different kinds of arms is presented, including the special cases of diblock copolymers and regular star polymers. The two different kinds of interactions between the substrate and the monomeric units which can be repulsive attractive or neutral combine in these heteroarm stars. They can act cooperatively or antagonistically determining, in connection with the effects of the architecture and the sizes of the branches, the mode of retention of the macromolecules. The compensation point, where no surface effects remain when the surface−monomer interactions are negligible, can also be reached by cancellation of the opposite but not negligible interactions of the two different kinds of arms with the substrate.

Dynamic Viscoelastic Properties of Multi-Arm Star Polystyrenes in the Molten State.

Multi-arm star polystyrenes with various lengths and number of arms were synthesized, and their dynamic viscoelastic properties were investigated in the molten state. The master curves of the storage modulus for the multi-arm stars showed a shoulder at low frequencies, suggesting that a new mechanical relaxation exists at the long time scales after completion of entanglement relaxation. The enhancement of the zero-shear viscosity compared with the regular star polymers was also observed for the multi-arm star polymers.

Controlling the self-assembly and dynamic response of star polymers by selective telechelic functionalization

We report on the structure and dynamics of model mono-, di-, and tri-ω-functionalized three-arm star polybutadiene melts. By using x-ray scattering and dynamic rheological measurements, we find that functionalization of the arm ends can lead to distinctly different supramolecular structures and material behavior. The monofunctionalized samples behave like multiarm nonionic star-like dendrimers, whereas the difunctional stars resemble a transient network consisting of highly branched structures with a very broad relaxation spectrum. On the other hand, the trifunctional stars seem to develop an unusually regular structure of dominant intramolecularly aggregated functional groups leading to collapsed star conformations, resembling soft spheres, and a well-defined terminal relaxation. These results suggest that by tailoring the telechelic functionalization of regular star polymers, a route to design and obtain a wealth of controlled supramolecular structures exhibiting a rich and variable dynamics could open.

Non-Newtonian viscosity in linear and star polymers

We theoretically investigate non-Newtonian viscosity and coil deformation of linear and (regular) star polymers in dilute solution subject to large shear rates. A bead-and-spring model with preaveraged hydrodynamic interaction, accounting also approximately for good-solvent expansion, is employed within the Rouse-Zimm approach. We impose a constraint on the average spring lengths, so as to keep constant the average contour length of the arms under shear: this corresponds to assuming that the springs become increasingly stiffer. For any topology and a very large molecular mass, coil deformation modifies the hydrodynamic interaction, that goes to a maximum, and then decreases with a crossover from the Zimm to the Rouse regime with increasing shear rate. Correspondingly, the intrinsic viscosity decreases and then raises above its low-shear value. This behavior is however much less pronounced under good-solvent conditions. At very large shear rate, the constraint on the spring lengths becomes the dominant factor. This leads to a decrease of intrinsic viscosity with an asymptotic –2/3 power law for any draining condition. Simultaneously, the strongly elongated coil becomes fully aligned with flow.

Molecular Shape of Regular Star Polymers by Monte Carlo Simulations

Off-lattice Monte Carlo simulations were performed on linear and 12-arm star polymers in a good-solvent and in the ϑ state to investigate both the molecular shape and the size distribution. We find that in a good solvent the star polymer is more spherical than a random walk, the more so the smaller its size is; moreover, a star of finite chain length in the ϑ state has a shape more similar to that in good solvent than to that in a random walk because of the excluded-volume restrictions that are particularly relevant in the core region. Both results are at variance with what is found in linear chains. Furthermore, the size distribution of the star is much narrower in a good solvent than in a random walk, approaching somewhat a δ function. This effect is also seen in the strong deformation of the density profile away from the center of mass.

Dynamics of regular star polymers: Viscoelasticity and oscillatory flow birefringence

The dynamics of linear and regular star polymers in a good solvent and in the Θ state is investigated theoretically considering the viscoelastic and the oscillatory flow birefringence response under an alternating shear deformation. We show that in a good solvent the phase angles of the viscoelastic and of the birefringence response are different. The physical reason of this difference is that viscoelasticity depends on the orientation of the chain stresses with the applied deformation, whereas birefringence measurements probe the orientation of the chain bonds. Only in the phantom chain the two orientations are the same, whereas this is no more true in a good solvent because of the long-range intramolecular interactions. Moreover, the phase angles show a maximum in the case of stars at ω≅1/τ1, where ω is the applied frequency and τ1 the longest relaxation time, that is strictly related to a shoulder in the imaginary part of the complex modulus. The reasons of this feature, which is absent in linear chains, are discussed in connection with the discrete spectrum of relaxation times.

Polymer dynamics in solution Universal properties vs. individual behaviour in a unified approach

The main factors affecting the dynamics of polymer chains in dilute solution are reviewed. We consider both the collective properties of the chain that follow relatively simple universal laws and the local properties related to the chain stereochemistry. Good-solvent expansion and hydrodynamic interaction are discussed for chains of different architecture, in particular linear and regular star polymers, starting from the usual Rouse–Zimm approach. We also include in the dynamic equations the effect of the local chain stiffness, arising from (i) the equilibrium configurational properties of the chain and (ii) the energy barriers to skeletal rotations hindering the propagation of conformational rearrangements along the chain backbone. The quantities taken into consideration are the intrinsic viscosity and the hydrodynamic radius, compared with the radius of gyration, as well as the complex modulus measured under an oscillating shear deformation, and the dynamic structure factor measured through quasi-elastic scattering. As an example of non-equilibrium behaviour, we discuss a theoretical investigation of the kinetics of chain contraction to a compact globular state following a sudden change in solvent quality.

Local Conformation of Regular Star Polymers in a Good Solvent: A Monte Carlo Study

Off-lattice Monte Carlo simulations were performed on linear and 12-arm regular star polymers with up to 472 repeat units in the excluded-volume regime. For both topologies, the overall size scales asymptotically with molecular weight through a Flory exponent, v = 0.588, but for finite molecular weights, the apparent exponent is slightly different in the case of the radius of gyration and of the root-mean-square end-to-end distance and definitely smaller in the case of the hydrodynamic radius. The interatomic distances within the star follow a 2-fold behavior, according to whether the two atoms belong to the same arm or to different arms. This result is related with the peculiar behavior of the scalar products among the bond vectors. If these belong to the same arm and are remote from the branch point, the scalar products follow the same pattern as in the linear chain. If however the bonds are close to the branch point, the scalar products are much larger and essentially constant, indicating a substantial arm stretching. Conversely, if the two bonds are on different arms, the scalar products across the branch point drop at once by more than 1 order of magnitude. Therefore, the initial arm directions are essentially noncorrelated, and the interarm repulsions are best accommodated with a minimum entropy loss.

Thermodynamic Properties of Dilute and Semidilute Solutions of Regular Star Polymers

The osmotic modulus of solutions of polybutadiene stars with f = 32, 64, and 128 arms have been measured from the dilute to the semidilute regime in the good solvent cyclohexane by static light scattering. Some complementary results on low molecular weight stars have been obtained using SANS. Values of the dimensionless virial ratio g ? A 3 /A 2 2 M0.62 for these many-arm stars accord well with the hard-sphere value (5/8). The concentration dependence of the osmotic modulus near the polymer coil overlap concentration, A 2 Mc 1, is characterized by a steep increase. This behavior agrees with arguments by Witten, Pincus, and Cates which indicate a steplike rise in the osmotic modulus where the step height scales as f 3/2 . In the semidilute regime the osmotic modulus becomes identical with that of a homogeneous linear polymer solution. A linear polybutadiene sample was also considered for comparison with the star polybutadiene measurements.

Dynamics of Regular Star Polymers: The Intrinsic Viscosity

The dynamics of a regular star polymer is investigated under good-solvent and Θ conditions. A self-consistent approach to the equilibrium and dynamics is proposed within the Gaussian approximation in terms of the polymer normal modes, i.e., suitable statistically-independent linear combinations of the bond vectors. The equilibrium normal modes used to study the star expansion through self-consistent free-energy minimization (see Allegra, G. ; Colombo, E. ; Ganazzoli, F. Macromolecules 1993, 26, 330) form a first-order approximation to the dynamical normal modes under partial-draining conditions. The latter modes are obtained by diagonalization of a matrix that depends on the intramolecular elasticity and on the hydrodynamic interaction in the preaveraging approximation, the effect of chain expansion on both being easily accounted for. If the equilibrium normal modes are used, the relaxation times, from which the intrinsic viscosity is calculated, are somewhat in error only for the collective modes describing the concerted motion of the arms, unlike those related with the independent motion of the arms ; on the other hand, they yield the intrinsic viscosity to a very good approximation, thus avoiding the lengthy diagonalization. Numerical results for regular stars and linear chains are summarized by analytical equations giving the mean-square radius of gyration , the hydrodynamic radius R H and the intrinsic viscosity [η]. The influence of the topology is expressed through the ratios g Q = Q star /Q lin , Q being any of the above quantities. In a good solvent, the star is only slightly more expanded than the linear chain, and so the g ratios are very close to the theoretical phantom-chain value both for (S 2 ) and for R H . Conversely, [η] increases less in the star than in the linear chain because of the different rate of change with expansion of the intramolecular elasticity and of the hydrodynamic interaction, and so the corresponding g ratio is lower than the phantom-chain value. In the Θ state, the residual three-body interactions give a finite expansion to the star, unlike the linear chain. Therefore, we have g Q ph ≤ g Q * and R H , in agreement with experiment (the asterisk refers to the good-solvent conditions) ; on the other hand, we get g η * < g η ph < g η Θ , whereas the experimental finding is g η * < g η Θ < g η ph . The reason for this discrepancy is attributed to the preaveraging approximation, which becomes questionable for stars in the Θ state because of their large density near the branch point.

Chain collapse of star polymers

AbstractThe self‐consistent approach to free‐energy optimization is applied to regular star polymers in bad solvents (T &lt; Θ); the Gaussian approximation and the Zimm‐Kilb description of Fourier modes are both warranted under these conditions leading to chain collapse. As currently done in this approach, the interatomic‐contact free energy is taken to be a single‐valued function of the mean‐square radius of gyration 〈S2〉, whence the universal plots of the mean‐square distances between two atoms and between the atoms and the center of mass are obtained as a function of the contraction ratio α = 〈S2〉/〈S2〉0 (the zero subscript denotes the unperturbed state at T = Θ) and of the degree of branching. The density as a function of the distance from the center of mass as well as the equilibrium structure factor are likewise evaluated. The decrease of αs with an increase of the undercooling (Θ − T) at a fixed molecular weight is sharper with a smaller number of arms, being sharpest with the linear chain. The relative fluctuation of the radius of gyration, expressed as (〈S4〉 − 〈S2〉2)/〈S2〉2, increases at first with the undercooling, showing a maximum close to the transition temperature which is more pronounced the smaller is the degree of branching, then decreases sharply at strong contration. The average location of the free ends of the collapsed molecule is close to, or even outside, the surface of the resulting globule, their mean‐square distance from the center of mass being 2 〈S2〉. Conversely, the mean‐square distance of the branch point from the center of mass if 2〈S2〉/f, f being the number of arms.