The interaction parameter of crosslinked networks and star polymers

Recent results on blends containing star polymers have revived the interest on the interaction parameters of structures that contain junctions between chains, a matter which can be connected with the earlier studies on the influence of crosslinks on the interaction parameters of polymer networks and gels. Here, we review results on crosslinked networks and star polymer solutions together with the more recent work on star polymer blends. The review covers swelling and elastic deformation of gels, differential vapour sorption between crosslinked and uncrosslinked polymers, osmotic equilibrium of gels and of star polymer solutions, and neutron scattering of polymer blends containing star polymers. In the systems reviewed, the interaction parameters of stars and networks differ from those of linear chains, and the difference is attributed mainly to entropic effects.     

Chain overlap and entanglements in dilute polymer solutions: Brownian dynamics simulation

We have analyzed chain conformations and the existence — or otherwise — of chain overlaps and entanglements in dilute polymer solutions (at concentrations c < C^*, c^* = critical concentration). The fundamental problem of existence of chain overlaps in dilute solutions is also related to the drag reduction phenomenon (DR). Some experimental results pertinent to DR are explained in terms of entanglements even for solutions at concentrations defined in ppm. We report results of Brownian dynamics simulations of polymer solutions in which the equations of motion of the chains are solved by using the Langevin equation. Chains move according to actions of a systematic frictional force and a randomly fluctuating force w(t), where t is time. In addition, a shear flow field can be introduced into the model. To evaluate the structure of polymer chains in solution we have devised a measure of interchain contacts and two different measures of entanglements. The results for c = 0.3 c^* demonstrate that both chain entanglements and overlaps take place even in dilute solution. They also confirm predictions from an earlier combinatorial model.     

Conformational properties and interaction of polyelectrolyte pH-sensitive stars

Changes in the conformations of two polyelectrolyte stars with amphiphilic segments during their convergence are investigated by the Scheutjens-Fleer method (a numerical method of solving self-consistent field equations). The stars are placed in an aqueous-salt solvent at a pH close to the pK of the segments of polyelectrolyte arms. Individual stars have a two-phase quasi-micellar conformation at a sufficiently strong hydrophobicity of segments in the uncharged state and at a sufficiently low salt concentration. This conformation is formed via separation of star arms into two groups: One consists of uncharged arms and forms a dense core in the star center, while the other consists of arms coming through and forming a corona with charged arms. When stars in this conformation converge, the transition of arms from the corona on the side of the oncoming star to the core occurs inside both stars. When stars touch each other with their cores, the stars merge into a united quasi-micelle. The free energy of interaction of stars is a nonmonotonic function of distance D between their centers. This value grows with a decrease in D until the cores come into contact. Upon the contact and merging of the cores, the free-energy values are characterized by a local minimum corresponding to an ellipsoid-shaped united quasi-micelle. With an increase in the concentration of salt in the solution, individual stars adopt extended conformations. In this case, the interaction of two stars is repulsive at all D values. However, if the salt concentration very slightly exceeds the threshold value of formation of a core in an isolated star, then the initially extended stars during their approach toward each other adopt (at first, each of them separately) a quasi-micellar conformation, while their cores grow as they converge and merge upon contact.     

Effect of the matrix on DNA electrophoretic mobility

DNA electrophoretic mobilities are highly dependent on the nature of the matrix in which the separation takes place. This review describes the effect of the matrix on DNA separations in agarose gels, polyacrylamide gels and solutions containing entangled linear polymers, correlating the electrophoretic mobilities with information obtained from other types of studies. DNA mobilities in various sieving media are determined by the interplay of three factors: the relative size of the DNA molecule with respect to the effective pore size of the matrix, the effect of the electric field on the matrix, and specific interactions of DNA with the matrix during electrophoresis.     

Colloidal properties of star polymers

Regular star polymers with functionality f = 64 and f = 128 have such high segment density that they resemble “hard sphere” objects in dilute solution. In semi-dilute solution they form a macrocrystalline ordered phase with spacings of the order of 100 to 500Å. They are physical gels. Their melt properties are characterized by a long term relaxation process not found in stars with fewer arms.     

Bimolecular radical termination: New perspectives and insights

The reversible addition‐fragmentation chain transfer‐chain length dependent termination (RAFT‐CLD‐T) method has allowed us to answer a number of fundamental questions regarding the mechanism of diffusion‐controlled bimolecular termination in free‐radical polymerization (FRP). We carried out RAFT‐mediated polymerizations of methyl acrylate (MA) in the presence of a star matrix to develop an understanding of the effect of polymer matrix architecture on the termination of linear polyMA radicals and compared this to polystyrene, polymethyl methacrylate, and polyvinyl acetate systems. It was found that the matrix architecture had little or no influence on termination in the dilute regime. However, due to the smaller hydrodynamic volumes of the stars in solution compared to linear polymer of the same molecular weight, the gel onset point occurred at greater conversions, and supported the postulate that chain overlap (or c*) is the main cause for the observed autoacceleration observed in FRP. Other theories based on “short–long” termination or free‐volume should be disregarded. Additionally, since our systems are well below the entanglement molecular weight, entanglements should also be disregarded as the cause of the gel onset. The semidilute regime occurs over a small conversion range and is difficult to quantify. However, we obtain accurate dependencies for termination in the concentrated regime, and observed that the star polymers (through the tethering of the arms) provided constriction points in the matrix that significantly slow the diffusion of linear polymeric radicals. Although, this could at first sight be postulated to be due to reptation, the dependencies showed that reptation could be considered only at very high conversions (close to the glass transition regime). In general, we find from our data that the polymer matrix is much more mobile than what is expected if reptation were to dominate. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 3155–3173, 2008     

Advances in DNA electrophoresis in polymer solutions.

DNA electrophoresis in gels and solutions of agarose and polyacrylamide was objectively evaluated with regard to separation efficiency at optimal polymer concentrations. In application to DNA fragments, polyacrylamide gels were superior for separating fragments of less than 7800 bp, and agarose gels are the best choice for larger fragments. Agarose solutions are nearly as good as polyacrylamide gels for small DNA (< 300 bp). Agarose solutions have a higher efficiency than polyacrylamide solutions for DNA of less than 1200 bp. Separation efficiency sharply decreases with increasing length of DNA. Retardation in polyacrylamide solutions was found to depend on polymer length in a biphasic fashion. The choice of resolving polymer concentrations depends on the progressive stretching of DNA in proportion to polymer concentration. The rate of that stretching appears higher in polyacrylmide solution than in gels or in liquid or gelled agarose. Application of polymer solutions to capillary electrophoresis raises further problems concerning agarose plugs, DNA interactions with the polymers, operation at low field strength and long durations as well as detection sensitivity.     

Synthesis and dilute solution properties of divinylbenzene-linked polystyrene stars with mixed arm lengths: Evidence for coupled stars

Sequential anionic polymerization of styrene and divinylbenzene (DVB) is known to lead to the formation of star-shaped polymers. This ‘arms-first’ method has been widely used and studied. It is known that this polymerization forms stars with anionically active cores. This article is concerned with the attempt to make asymmetric-star polymers utilizing these living carbanionic sites present in the core to form a second set of shorter arms growing out from the star core. The presence of remaining unreacted DVB within the core was found to cause the stars to couple to form linked double stars and other larger structures. Results from detailed dilute solution studies of the resulting polymers are reported. It was found that the results obtained from size exclusion chromatography for the double stars were flow rate dependent; only at low flow rates was a true size separation obtained. © 1997 John Wiley & Sons, Inc.     

Synthesis,purification, and characterization of “perfect” star polymers via “Click” coupling

The copper (I)‐catalyzed azide‐alkyne cycloaddition “click” reaction was successfully applied to prepare well‐defined 3, 6, and 12‐arms polystyrene and polyethylene glycol stars. This study focused particularly on making “perfect” star polymers with an exact number of arms, as well as developing techniques for their purification. Various methods of characterization confirmed the star polymers high purity, and the structural uniformity of the generated star polymers. In particular, matrix‐assisted laser desorption ionization‐time‐of‐flight mass spectrometry revealed the quantitative transformation of the end groups on the linear polymer precursors and confirmed their quantitative coupling to the dendritic cores to yield star polymers with an exact number of arms. In addition to preparing well‐defined polystyrene and poly(ethylene glycol)homopolymer stars, this technique was also successfully applied to amphiphilic, PCL‐b‐PEG star polymers. © 2011 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012     

Rheology of polymers that are initially in the disentangled state

An attempt was made to measure the effects of molecular entanglements on the rheological properties of polymer melts. Two classes of polymers were studied; glassy atactic polystyrene polymers covering a 60-fold range in molecular weight, and semicrystalline high-density polyethylene from two sources covering about a twofold range in molecular weight. The entanglements initially present were removed or greatly reduced in number by freeze drying the polystyrene polymers from dilute solutions below and above C*, the critical overlap concentration, and by slowly crystallizing the polyethylene from very dilute solutions. Since only minor rheological changes were observed with polystyrene, it would appear that the initially isolated coils interpenetrate more rapidly than is indicated by the results of Liu and Morawetz, or that the rheological behavior is rather insensitive to whether the flow obstacles are intermolecular or intramolecular. The enhancement of the viscosity and elasticity observed with polyethylene polymers indicate the importance of the crystallization step on the local melt topology of the polymer chains.     

Nuclear magnetic resonance relaxation studies of polyacrylamide solution

 The cohesive interaction among polymer chains in a polyacrylamide (PAAm)–D₂O solution has been studied by NMR relaxation. The NMR relaxation times of PAAm in the good solvent D₂O were measured at different temperatures. The results show that the solution system has a high local viscosity and that its relaxation characteristic is soft-solid-like. The temperature dependence of the relaxation behavior of the solution is obviously different from that of ordinary polymer solutions. The difference lies in the relaxation behavior of the methylene protons in the main chain of PAAm, as shown by analyzing the relaxation process with single exponential and biexponential decays. As the temperature increases, the solvation is weakened, leading polymer chains to form curling coils, thus hindering the movement of the methylene protons among the main chains. It can be expected from the existence of 80% fast-relaxing protons that there are a zhigh number of entanglements among the polymer chains in PAAm solution. The information about entanglements among the polymer chains can be deduced from the biexponential dependence of the spin–spin relaxation on the concentration of the polymer solutions. Received: 14 April 1999/Accepted in revised form: 12 October 1999     

Behavior of Aqueous Solutions of Thermosensitive Starlike Polyalkyloxazolines with Different Arm Structures

The behavior of aqueous solutions of starlike polyalkyloxazolines with a calix[8]arene core is investigated by light scattering and turbidimetry. Polyethyloxazoline, the gradient copolymer of ethyloxazoline and isopropyloxazoline, and the block copolymers of polyethyloxazoline and polyisopropyloxazoline are used as arms. Using the methods of molecular hydrodynamics and optics, it is shown that the arms of the studied stars are strongly folded in organic solvents. It is found that the structure of arms affects the processes of self-organization and aggregation of their macromolecules in aqueous solutions. At room temperature, the dimensions of aggregates and their fraction in solutions depend on the position of ethyloxazoline and isopropyloxazoline units with respect to the calixarene core. Introducing ethyloxazoline units into macromolecules is accompanied by an increase in both the phase-separation temperature and the width of this interval relative to the corresponding characteristics of the star with polyisopropyloxazoline arms. For stars with copolymer arms, the temperatures of the end of phase transition differ insignificantly. Differences in the behavior of the studied arms are due to the fact that the dehydration temperature for polyethyloxazoline is noticeably higher than that for polyisopropyloxazoline.     

The Mechanical Strength of a Mechanical Bond: Sonochemical Polymer Mechanochemistry of Poly(catenane) Copolymers

Topological molecular connections and structures, including physical entanglements in polymer networks, knots along polymer chains, and rotaxanes in sliding ring gels, have important consequences for the physical properties of polymeric materials. Often these topologies contribute through their ability to bear mechanical stress, but experimental measures of their relative mechanical strength are rare. Here, we use sonochemical polymer mechanochemistry to assess the relative mechanical strength of a multicatenane copolymer relative to copolymers of cyclic and linear analogs. The relative mechanical strengths are obtained by comparing the limiting molecular weights (M_lim) and contour lengths (L_lim) of the polymers under pulsed ultrasound of their dilute solutions. The values of M_lim and L_lim, and thus the inferred mechanical strengths of the polymers, are effectively identical. The mechanical bonds of the catenanes are therefore as strong, or stronger, mechanically as the covalent bonds along the polymer backbone.     

Phase behavior and viscoelastic properties of entangled block copolymer gels

Triblock copolymers in midblock‐selective solvents can form physical gels. However, at low triblock contents (near the percolation threshold), the bridging of chains between micelles can lead to macrophase separation. Adding a styrene–isoprene diblock to a styrene–isoprene–styrene triblock copolymer in squalane can eliminate macrophase separation, yielding a wide range of stable, single‐phase gels with a disordered arrangement of micelles. The plateau modulus of these triblock gels scales with the 2.2 power of polymer content, indicating the importance of entanglements in dictating the modulus. Comparing gels made from the midblock‐saturated derivative of the same polymer [styrene‐(ethylene‐alt‐propylene)‐styrene] in squalane reveals that the modulus differences in the gels are a direct consequence of the difference in the entanglement molecular weight of the midblock homopolymer in bulk. Finally, the broad relaxation spectrum of these triblocks is well‐described by a recent theory for the dynamics of entangled star polymers, with the breadth of the relaxation spectrum dictated by the number of entanglements per midblock in the gel. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2183–2197, 2001     

Dynamics of star branched polymers in a matrix of linear chains — a Monte Carlo study

A simple cubic lattice model of the melt of 3-arm star-branched polymers of various length dissolved in a matrix of long linear chains (n₁ = 800 beads) is studied using a dynamic Monte Carlo method. The total polymer volume fraction is equal to 0,5, while the volume fraction of the star polymers is about ten times smaller. The static and dynamic properties of these systems are compared with the corresponding model systems of isolated star-branched polymers and with the melt of linear chains. It has been found that the number of dynamic entanglements for the star polymers with arm length up to 400 segments is too small for the onset of the arm retraction mechanism of polymer relaxation. In this regime dynamics of star-branched polymers is close to the dynamics of linear polymers at corresponding concentration and with equivalent chain length. The entanglement length for star polymers appears to be somewhat larger compared with linear chains.     

Systematic study of field and concentration effects in capillary electrophoresis of DNA in polymer solutions

A systematic study of the separation of double-stranded DNA in hydroxypropylcellulose (HPC) with a molecular mass of 10⁶ was undertaken, using a variety of concentrations (from 0.1 to 1%) and different electric fields (from 6 to 540 V/cm). The data show that a high polymer concentrations (0.4%) and low fields, the separation mechanism is similar to that occurring in gels. The results are in good agreement with theoretical models, and in particular with a recently proposed theory for gels with a pore size smaller than the persistence length of DNA. For more dilute solutions and high fields, however, the separation pattern cannot be explained by existing theories. The existence of an original mechanism was confirmed by the direct observation of the conformation of double-stranded DNA molecules in the polymer solution by fluorescence videomicroscopy. Practical conclusions for the capillary electrophoretic separation of duplex DNA are drawn.     

Tracer diffusion of star-branched polystyrenes in poly(vinyl methyl ether) gels

The tracer diffusion of 3-, 4-, and 12-arm polystyrene (PS) stars in poly(vinyl methyl ether) (PVME) gels has been measured by dynamic light scattering (DLS). The intensity correlation functions were analyzed by two methods. One was that employed previously in a DLS study of linear PS diffusion in PVME gels [N. A. Rotstein and T. P. Lodge, Macromolecules, Vol. 24. p. 1316 (1992)], and the other was based on consideration of possible nonergodicity effects [P. N. Pusey and W. van Megen, Physica A, Vol. 157, p. 705 (1990)]. Both methods gave equivalent results, suggesting that nonergodicity plays a small role in this system. This conclusion is not unreasonable, given that the PVME gels are almost isorefractive with the solvent (toluene), and that the signal is dominated by scattering from the PS chains. The resulting star diffusivities are consistently less than or equal to those for linear probes of comparable size, with the difference increasing with molecular weight. The diffusivities are also less than or equal to those obtained for the same stars in PVME solutions. A weak dependence on the number of arms is also observed. Finally, the mobility of a given star in a gel is much more sensitive to variations in the average molecular weight between cross-links than is the mobility of a linear chain. All of these features in the data are broadly consistent with the reptation hypothesis. © 1993 John Wiley & Sons, Inc.     

Influence of branch length asymmetry on the electrophoretic mobility of rigid rod-like DNA

The electrophoretic mobility of three-arm asymmetric star DNA molecules, produced by incorporating a short DNA branch at the midpoint of rigid-rod linear DNA fragments, is investigated in polyacrylamide gels. We determine how long the added branch must be to separate asymmetric star DNA from linear DNA with the same total molecular weight. This work focuses on two different geometric progressions of small DNA molecules. First, branches of increasing length were introduced at the center of a linear DNA fragment of constant length. At a given gel concentration, we find that relatively small branch lengths are enough to cause a detectable reduction in electrophoretic mobility. The second geometric progression starts with a small branch on a linear DNA fragment. As the length of this branch is increased, the DNA backbone length is decreased such that the total molar mass of the molecule remains constant. The branch length was then increased until the asymmetric branched molecule becomes a symmetric three-arm star polymer, allowing the effect of molecular topology on mobility to be studied independent of size effects. DNA molecules with very short branches have a mobility smaller than linear DNA of identical molar mass. The reason for this change in mobility when branching is introduced is not known, however, we explore two possible explanations in this article. (i) The branched DNA could have a greater interaction with the gel than linear DNA, causing it to move slower; (ii) the linear DNA could have modes of motion or access to pores that are unavailable to the branched DNA.     

Synthesis and characterization of star-shaped polytetrahydrofuran

Star polymers of tetrahydrofuran (polyTHF) were prepared by reaction of living polyTHF with diethylene triamine (DETA) in the presence of 2,2,6,6-tetramethylpiperidine (TMP) as proton trap. The influence of several reaction parameters on the end-capping reaction was studied in order to produce stars having varying number of arms. With a starting living polyTHF with a molecular weight of 1600, star-shaped polymers containing up to seven polymer chains could be prepared. When the molecular weight of the living polyTHF was 8000, at most five polymer chains could be grafted on the DETA. Some physical properties of the star polymers were compared with those of their linear counterparts of the same molecular weight.     

Sparsely cross-linked "nanogels" for microchannel DNA sequencing

We have developed sparsely cross-linked "nanogels", sub-colloidal polymer structures composed of covalently linked, linear polyacrylamide chains, as novel DNA sequencing matrices for capillary electrophoresis. The presence of covalent cross-links affords nanogel matrices with enhanced network stability relative to standard, linear polyacrylamide (LPA), improving the separation of large DNA fragments. Nanogels were synthesized via inverse emulsion (water-in-oil) copolymerization of acrylamide and N,N-methylenebisacrylamide (Bis). In order to retain the fluidity necessary in a replaceable polymer matrix for capillary array electrophoresis (CAE), a low percentage of the Bis cross-linker (< 10(-4) mol%) was used. Nanogels were characterized by multiangle laser light scattering and rheometry, and were tested for DNA sequencing by CAE with four-color laser-induced fluorescence (LIF) detection. The properties and performance of nanogel matrices were compared to those of a commercially available LPA network, which was matched for both weight-average molar mass (Mw) and extent of interchain entanglements (c/c*). Nanogels presented in this work have an average radius of gyration of 226 nm and a weight-average molar mass of 8.8 x 10(6) g/mol. At concentrations above the overlap threshold, nanogels form a clear, viscous solution, similar to the LPA matrix (Mw approximately 8.9 x 10(6) g/mol). The two matrices have similar flow and viscosity characteristics. However, because of the physical network stability provided by the internally cross-linked structure of the nanogels, a substantially longer read length ( approximately 63 bases, a 10.4% improvement) is obtained with the nanogel matrix at 98.5% accuracy of base-calling. The nanogel network provides higher-selectivity separation of ssDNA sequencing fragments longer than 375 bases. Moreover, nanogel matrices require 30% less polymer per unit volume than LPA. This is the first report of a sequencing matrix that provides better performance than LPA, in a side-by-side comparison of polymer matrices matched for Mw and extent of interchain entanglements.