Absolute negative mobility of active polymer chains in steady laminar flows

The mechanical response of dielectric elastomers can be influenced or even controlled by an imposed electric field. It can, for example, cause mechanical stress or strain without any applied load; this phenomenon is referred to as electrostriction. There are many purely phenomenological hyperelastic models describing this electroactive response of dielectric elastomers. In this contribution, we propose an electromechanical constitutive model based on molecular chain statistics. The model considers polarization of single polymer chain segments and takes into account their directional distribution. The latter results from non-Gaussian chain statistics, taking finite extensibility of polymer chains into account. The resulting (one-dimensional) electric potential of a single polymer chain is further generalized to the (three-dimensional) network potential. To this end, we apply directional averaging on the basis of numerical integration over a unit sphere. In a special case of the eight-direction (Arruda–Boyce) model, directional averaging is obtained analytically. This results in an invariant-based electroelastic constitutive model of dielectric elastomers. The model includes a small number of physically interpretable material constants and demonstrates good agreement with experimental data, with respect to the electroactive response and electrostriction of dielectric elastomers.

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Direct observation of morphological transition for an adsorbed single polymer chain

Scientific Reports ◽

10.1038/s41598-020-77761-0 ◽

2020 ◽

Vol 10 (1) ◽

Author(s):

Yukari Oda ◽

Daisuke Kawaguchi ◽

Yuma Morimitsu ◽

Satoru Yamamoto ◽

Keiji Tanaka

Keyword(s):

Polymer Chain ◽

Synthetic Polymer ◽

Polymer Chains ◽

Dynamics Simulation ◽

Morphological Transition ◽

Nano Composite ◽

Force Microscopy ◽

Local Conformation ◽

Atomic Force ◽

Single Polymer Chain

AbstractA better understanding of the structure of polymers at solid interfaces is crucial for designing various polymer nano-composite materials from structural materials to nanomaterials for use in industry. To this end, the first step is to obtain information on how synthetic polymer chains adsorb onto a solid surface. We closely followed the trajectory of a single polymer chain on the surface as a function of temperature using atomic force microscopy. Combining the results with a full-atomistic molecular dynamics simulation revealed that the chain became more rigid on the way to reaching a pseudo-equilibrium state, accompanied by a change in its local conformation from mainly loops to trains. This information will be useful for regulating the physical properties of polymers at the interface.

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A non-local diffusion equation arising in terminally attached polymer chains

European Journal of Applied Mathematics ◽

10.1017/s0956792500000267 ◽

1990 ◽

Vol 1 (4) ◽

pp. 311-326 ◽

Cited By ~ 1

Author(s):

Xinfu Chen ◽

Avner Friedman

Keyword(s):

Field Theory ◽

Diffusion Equation ◽

Polymer Chain ◽

Mean Field Theory ◽

Mean Field ◽

Polymer Melt ◽

Polymer Chains ◽

Number Density ◽

Non Local ◽

Local Diffusion

We consider a polymer melt in a domain Ω whereby each polymer chain is attached at one endpoint to a fixed surface S contained in ∂Ω. Denote by G(x, t;y) the normalized number density of all subchains from x to y of length t. Then, according to the selfconsistent mean field theory, G satisfies, for each y: Gt - Δ2G + σϕG = 0, where σ is a real parameter, and ϕ is a functional of G(·, ·; ·) both non-local and nonlinear. We establish the existence of G and C∞ regularity of ϕ, as a function of x.

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Viscoelasticity of a stretched polymer chain with ends exposed to a constant force

Polymer Science Series A ◽

10.1134/s0965545x11110010 ◽

2011 ◽

Vol 53 (11) ◽

pp. 1086-1096 ◽

Cited By ~ 2

Author(s):

N. K. Balabaev ◽

I. P. Borodin ◽

T. I. Borodina ◽

T. N. Khazanovich

Keyword(s):

Polymer Chain ◽

Constant Force

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Planar flows past thin multi-blade configurations

Journal of Fluid Mechanics ◽

10.1017/s0022112096007951 ◽

1996 ◽

Vol 324 ◽

pp. 355-377 ◽

Cited By ~ 13

Author(s):

F. T. Smith ◽

S. N. Timoshin

Keyword(s):

Boundary Layer ◽

Numerical Solutions ◽

Reynolds Numbers ◽

Laminar Flows ◽

Two Dimensional ◽

Boundary Layer Equations ◽

Require Solution ◽

Lift And Drag ◽

Planar Flows ◽

Steady Laminar

Two-dimensional steady laminar flows past multiple thin blades positioned in near or exact sequence are examined for large Reynolds numbers. Symmetric configurations require solution of the boundary-layer equations alone, in parabolic fashion, over the successive blades. Non-symmetric configurations in contrast yield a new global inner–outer interaction in which the boundary layers, the wakes and the potential flow outside have to be determined together, to satisfy pressure-continuity conditions along each successive gap or wake. A robust computational scheme is used to obtain numerical solutions in direct or design mode, followed by analysis. Among other extremes, many-blade analysis shows a double viscous structure downstream with two streamwise length scales operating there. Lift and drag are also considered. Another new global interaction is found further downstream. All the interactions involved seem peculiar to multi-blade flows.

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PHOTOLYSIS OF POLYMETHACRYLIC ACID IN AQUEOUS SOLUTIONS

Canadian Journal of Chemistry ◽

10.1139/v64-076 ◽

1964 ◽

Vol 42 (3) ◽

pp. 522-531 ◽

Cited By ~ 9

Author(s):

C. H. Chou ◽

H. H. G. Jellinek

Keyword(s):

Aqueous Solutions ◽

Chain Length ◽

Polymer Chain ◽

Irradiation Time ◽

Polymer Concentration ◽

Chain Scission ◽

Polymer Chains ◽

Polymethacrylic Acid ◽

Degree Of Ionization ◽

Ph Values

The photolysis of polymethacrylic acid was studied in aqueous solutions as a function of pH, polymer concentration, polymer chain length, and small additions of electrolytes in the absence of oxygen with light of wavelength 2537 Å. The random chain scission constants decrease with increasing pH values. Small variations in polymer chain length and concentration and electrolyte concentration have no effect on the photolysis. Changes in the ultraviolet spectra with irradiation time are more pronounced at low pH values than higher ones. It is shown that the decrease in susceptibility to photolysis with increasing degree of ionization of the acid is not proportional to the decrease or increase of the number of COOH or COO− groups respectively. It is rather due to the same causes—that is changes in ionic atmosphere— which make the polymer chains uncoil with increasing ionization.

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