## A04 SAKAUE, Takahiro |Proposed Research Projects (2014-2015)

### Paper | Original Paper

#### 2015

Michiel Laleman, Marco Baiesi, Boris P. Belotserkovskii, Takahiro Sakaue, Jean-Charles Walter,and *Enrico Carlon,
Torque-Induced Rotational Dynamics in Polymers: Torsional Blobs and Thinning,
Macromolecules 49, 405-414 (2015).

[Summary] By using the blob theory and computer simulations, we investigate the properties of a linear polymer performing a stationary rotational motion around a long impenetrable rod. In particular, in the simulations the rotation is induced by a torque applied to the end of the polymer that is tethered to the rod. Three different regimes are found, in close analogy with the case of polymers pulled by a constant force at one end. For low torques the polymer rotates maintaining its equilibrium conformation. At intermediate torques the polymer assumes a trumpet shape, being composed by blobs of increasing size. At even larger torques the polymer is partially wrapped around the rod. We derive several scaling relations between various quantities as angular velocity, elongation, and torque. The analytical predictions match the simulation data well. Interestingly, we find a “thinning” regime where the torque has a very weak (logarithmic) dependence on the angular velocity. We discuss the origin of this behavior, which has no counterpart in polymers pulled by an applied force.

*Takuya Saito, *Takahiro Sakaue,
Driven anomalous diffusion: An example from polymer stretching,
Physical Review E 92, 012601/1-13 (2015).

[Summary] The way tension propagates along a chain is a key to govern many anomalous dynamics in macromolecular systems. After introducing the weak and the strong force regimes of the tension propagation, we focus on the latter, in which the dynamical fluctuations of a segment in a long polymer during its stretching process is investigated. We show that the response, i.e., average drift, is anomalous, which is characterized by the nonlinear memory kernel, and its relation to the fluctuation is nontrivial. These features are discussed on the basis of the generalized Langevin equation, in which the role of the temporal change in spring constant due to the stress hardening is pinpointed. We carried out the molecular dynamics simulation, which supports our theory.

#### 2014

Ahmed Khorshid, Philip Zimny, David Tetreault-La Roche, Geremia Massarelli, *Takahiro Sakaue, and *Walter Reisner,
Dynamic Compression of Single Nanochannel Confined DNA via a Nanodozer Assay,
Physical Review Letters 113, 268104:1-5 (2014).

[Summary] We show that a single DNA molecule confined and extended in a nanochannel can be dynamically compressed by sliding a permeable gasket at a fixed velocity relative to the　stationary polymer. The gasket is realized experimentally by optically trapping a nanosphere inside a nanochannel. The trapped bead acts like a nanodozer," directly applying compressive forces to the molecule without requirement of chemical attachment. Remarkably, these strongly non-equilibrium measurements can be quantified via a simple nonlinear convective-diffusion formalism and yield insights into the local blob statistics, allowing us to conclude that the compressed nanochannel-confined chain exhibits mean-field behaviour.

*Miho Yanagisawa, Shinpei Nigorikawa, Takahiro Sakaue, Kei Fujiwara, and Masayuki Tokita,
Multiple patterns of polymer gels in microspheres due to the interplay among phase separation, wetting, and gelation,
Proc. Natl. Acad. Sci. USA 111, 15894-15899 (2014).

[Summary] We investigate how microdroplet confinement affects pattern formation of a polymer blend in the liquid-and-gel coexisting phase, wherein interactions between the droplet surface and the polymers regulate wettability of the gelation polymer. The complete and partial wetting of the polymers produces two stable states: hollow microspheres and hemisphere microgels. In addition, gelation during phase separation produces various shapes as trapped states. The relation between capsule thickness and droplet size is changed by the dynamical coupling. Furthermore, multiple patterns with spherical asymmetric shapes are produced by the partial wetting and shape deformation along the phase boundaries between the sol/gel phases. These findings reveal a complex pattern formation arising from the interplay among the interfacial tensions, gel elasticity, and wetting in microspheres.

Ken-ichi Mizuochi, Hiizu Nakanishi, and *Takahiro Sakaue,
Dynamical scaling of polymerized membranes,
Europhysics Letters 107, 38003:p1 -p6 (2014).

[Summary] Monte Carlo simulations have been performed to analyze the sub-diffusion dynamics of a tagged monomer in self-avoiding polymerized membranes in the flat phase. By decomposing the mean square displacement into the out-of-plane (//) and the in-plane (⊥) components, weobtain good data collapse with two distinctive diffusion exponents 2 \alpha_{//} = 0.36 ± 0.01 and 2 \alpha_{⊥} =0.21 ± 0.01, and the roughness exponents \zeta_{//} = 0.6 ± 0.05 and \zeta_{⊥ }= 0.25 ± 0.05, respectively foreach component. Their values are consistent with the relation from the rotational symmetry. We derive the generalized Langevin equations to describe the sub-diffusional behaviors of a tagged monomer in the intermediate time regime where the collective effect of internal modes in the membrane dominate the dynamics to produce negative memory kernels with a power law. Wealso briefly discuss how the long-range hydrodynamic interactions alter the exponents.