Electron-Hole coherence and charging effects in ultrasmall metallic grains Academic Article uri icon


  • The dynamics of a polymer network are studied by direct view observation of the motion of a single point within a single polymer. Taking advantage of rather rigid biological microtubules as a case study, we expand the space and time scales of the system to those accessible by optical microscopy and standard video tools. Tracking is achieved by chemically attaching an optically resolved microsphere to a single point on the filament. We study the time dynamics of this point, without spatial averaging inherent in scattering methods. It is shown that the mean square displacement of the individual point is sensitive to local filament and network properties. [S0031-9007(97)05158-2] PACS numbers: 83.10.Nn An essential physical question in the study of polymer dynamics is how to relate the bulk rheological response of a network to the molecular-scale motions executed by an individual monomer. The latter are driven by random thermal collisions with the surrounding solvent molecules, and constrained at two levels: the embedding of the monomer within the polymer and the entanglement of the polymer within the network. In conventional chemical polymers the relevant length scales are on the order of 1 nm, far too small to be resolved by direct imaging techniques. Typical methods of study include light and neutron scattering, which are sensitive to local fluctuations in the density of the bulk sample. Light scattering can provide superb time resolution, while the few-angstrom wavelength of neutrons offers much improved spatial sensitivity. Nonetheless, these methods make a spatial averaging of the fluctuations taking place in a large volume of the sample. Attention is typically focused on the time domain, with use of fluctuation-dissipation arguments to relate modes of response to the thermally generated fluctuations. Recently, there have been a number of attempts to investigate local dynamics by direct imaging methods. The main trend has been to exploit biological polymers for their relative stiffness compared to simple synthetic ones, and also for their intrinsic biophysical interest. One approach has been to fluorescently label an entire polymer and watch its motion using video microscopy. The polymer is analyzed by measuring the wave vector [1] or the cosine correlation function [2]. In these methods the dynamics of a monomer is studied implicitly by measuring the dynamics of the entire polymer. Another method has been to implant a large bead in a network and investigate its restricted diffusion due to collisions with the surrounding filaments [3]. In this method, interpretation in terms of single filament dynamics must involve some a priori assumption. The approach described here is to prepare a system in which it is possible to image monomer motion directly, and to study the polymer network via the dynamics of a single monomer [4]. To this end, we expand the size and time scales of the system by exploiting biological polymers known as microtubules. These self-assembling filaments are stiff enough to maintain an average direction from end to end, yet sufficiently flexible to display thermally driven undulations. We “tag” a single monomer by attaching to it an optically resolvable bead (Fig. 1) and trace the bead’s position by video analysis. The motion of the bead displays the thermally driven motion of the microtubule itself. Using the clock provided by the video frame rate, we measure the mean square displacement (MSD) vs time interval of the bead. Classical random walk diffusion predicts that the MSD grows linearly in time, and our results lie in the deviations from this familiar situation. We interpret the data to probe the internal state of the network, e.g., to detect entanglement or quenched stress. Background for this experiment is set by considering a bead attached to a single microtubule whose dynamics are governed by thermally driven bending fluctuations. The important parameters governing the MSD at a point

publication date

  • January 1, 1998