Dynamic properties of low- and moderate-molecular-weight polystyrenes at infinite dilution

Simulational Tests of the Rouse Model

An extensive review of literature simulations of quiescent polymer melts is given, considering results that test aspects of the Rouse model in the melt. We focus on Rouse model predictions for the mean-square amplitudes ⟨(Xp(0))2⟩ and time correlation functions ⟨Xp(0)Xp(t)⟩ of the Rouse mode Xp(t). The simulations conclusively demonstrate that the Rouse model is invalid in polymer melts. In particular, and contrary to the Rouse model, (i) mean-square Rouse mode amplitudes ⟨(Xp(0))2⟩ do not scale as sin-2(pπ/2N), N being the number of beads in the polymer. For small p (say, p≤3) ⟨(Xp(0))2⟩ scales with p as p-2; for larger p, it scales as p-3. (ii) Rouse mode time correlation functions ⟨Xp(t)Xp(0)⟩ do not decay with time as exponentials; they instead decay as stretched exponentials exp(-αtβ). β depends on p, typically with a minimum near N/2 or N/4. (iii) Polymer bead displacements are not described by independent Gaussian random processes. (iv) For p≠q, ⟨Xp(t)Xq(0)⟩ is sometimes non-zero. (v) The response of a polymer coil to a shear flow is a rotation, not the affine deformation predicted by Rouse. We also briefly consider the Kirkwood-Riseman polymer model.

Multi-resolution polymer Brownian dynamics with hydrodynamic interactions

A polymer model given in terms of beads, interacting through Hookean springs and hydrodynamic forces, is studied. A Brownian dynamics description of this bead-spring polymer model is extended to multiple resolutions. Using this multiscale approach, a modeller can efficiently look at different regions of the polymer in different spatial and temporal resolutions with scalings given for the number of beads, statistical segment length, and bead radius in order to maintain macro-scale properties of the polymer filament. The Boltzmann distribution of a Gaussian chain for differing statistical segment lengths gives a diffusive displacement equation for the multi-resolution model with a mobility tensor for different bead sizes. Using the pre-averaging approximation, the translational diffusion coefficient is obtained as a function of the inverse of a matrix and then in closed form in the long-chain limit. This is then confirmed with numerical experiments.

Brownian dynamics study of polymer-stabilized nanoparticles

A Brownian dynamics simulation was carried out for a spherical nanoparticle with polymer chains tethered to its surface. These simulations are relevant to understanding the transport properties of polymer-stabilized nanoparticles in environmental and other applications. Hydrodynamic interactions (HI) were taken into account to properly describe the diffusion properties of a stabilized particle. HI are important in this context because of the close proximity of the surface-tethered polymer chains. HI were implemented using a method introduced by Fixman (1986 Macromolecules 19 1204), which uses a Chebyshev polynomial expansion to calculate the square root of the diffusion tensor. Simulation predictions were compared to published experimental data for the hydrodynamic radius of a silica particle stabilized by polystyrene tethered chains, and good agreement was achieved. A relationship that allows polymer-stabilized particles with arbitrary polymer-chain densities to be modelled is developed.

Properties of solid supports

Many supports including composite materials and functionalized surfaces are available for solid-phase synthesis. In the process of selecting the proper support it is important to consider the optimal performance during solid-phase synthesis. For most purposes the mechanically stable beaded gel resins are preferred. These resins are homogeneous, and the loading and physical and chemical properties can easily be varied. Optimal properties have been obtained by radical polymerization of end group acryloylated long-chain polyethylene glycols. However, polystyrene resins or amide bond free PEG-based resins may be more suited for general organic synthesis where reactivity of radicals, carbenes, carbanions, carbenium ions, or strong Lewis acids have to be considered. Loading of the resins can have a dramatic effect on the outcome of a synthesis and has to be considered separately for each synthesis. Synthesis of long peptides with 50-100 amino acids imposes completely different requirements on the performance, swelling, and loading than a large-scale synthesis of, for example, the pentapeptide enkephalin. Automated multiple synthesizers constructed for columns of beaded gel or composite supports are available from many suppliers. It is therefore expected that the optimization of support properties will continue in order to meet new synthetic challenges. In the synthesis for solid-phase screening of binding of biomolecules to ligands directly on the resin beads, it is an advantage if the resin is not permeable to the biomolecule so unbound molecules can easily be removed by washing. This is the case with polystyrene-based resins, but they do, however, often show nonspecific adhesion of proteins owing to the hydrophobic character of the polystyrene. Modification of the functional groups of polystyrene with polyethylene glycol as spacers for synthesis of the binding ligands can increase the available ligand concentration on the bead surface and eliminate most of the nonspecific adhesion. In contrast to binding studies, solid-phase assays of enzymes require beads that are permeable to the enzyme, as the progress of reaction can be followed and the product of reaction analyzed. The available amount on the surface of the polystyrene-based beads (approximately 0.3%) is not enough for product analysis. Therefore, in the case of enzyme assays, highly swelling permeable PEG-based gel resins or functionalized surfaces of a polar and porous matrix are preferred.

The dynamics of partially extended single molecules of DNA

The behaviour of an isolated polymer floating in a solvent forms the basis of our understanding of polymer dynamics. Classical theories describe the motion of a polymer with linear equations of motion, which yield a set of 'normal modes', analogous to the fundamental frequency and the harmonics of a vibrating violin string. But hydrodynamic interactions make polymer dynamics inherently nonlinear, and the linearizing approximations required for the normal-mode picture have therefore been questioned. Here we test the normal-mode theory by measuring the fluctuations of single molecules of DNA held in a partially extended state with optical tweezers. We find that the motion of the DNA can be described by linearly independent normal modes, and we have experimentally determined the eigenstates of the system. Furthermore, we show that the spectrum of relaxation times obeys a power law.