TY - JOUR

T1 - Branched droplet clusters and the Kramers theorem

AU - Frenkel, Mark

AU - Fedorets, Alexander A.

AU - Shcherbakov, Dmitry V.

AU - Dombrovsky, Leonid A.

AU - Nosonovsky, Michael

AU - Bormashenko, Edward

N1 - Publisher Copyright:
© 2022 American Physical Society.

PY - 2022/5

Y1 - 2022/5

N2 - Scaling laws inherent for polymer molecules are checked for the linear and branched chains constituting two-dimensional (2D) levitating microdroplet clusters condensed above the locally heated layer of water. We demonstrate that the dimensionless averaged end-to-end distance of the droplet chain r¯ normalized by the averaged distance between centers of the adjacent droplets l¯ scales as r¯/l¯∼n0.76, where n is the number of links in the chain, which is close to the power exponent ¾, predicted for 2D polymer chains with excluded volume in the dilution limit. The values of the dimensionless Kuhn length b ≅2.12±0.015 and of the averaged absolute value of the bond angle of the droplet chains |θ|¯=22.0±0.50 are determined. Using these values we demonstrate that the predictions of the Kramers theorem for the gyration radius of branched polymers are valid also for the branched droplets' chains. We discuss physical interactions that explain both the high value of the power exponent and the applicability of the Kramers theorem including the effects of the excluded volume, surrounding droplet monomers, and the prohibition of extreme values of the bond angle.

AB - Scaling laws inherent for polymer molecules are checked for the linear and branched chains constituting two-dimensional (2D) levitating microdroplet clusters condensed above the locally heated layer of water. We demonstrate that the dimensionless averaged end-to-end distance of the droplet chain r¯ normalized by the averaged distance between centers of the adjacent droplets l¯ scales as r¯/l¯∼n0.76, where n is the number of links in the chain, which is close to the power exponent ¾, predicted for 2D polymer chains with excluded volume in the dilution limit. The values of the dimensionless Kuhn length b ≅2.12±0.015 and of the averaged absolute value of the bond angle of the droplet chains |θ|¯=22.0±0.50 are determined. Using these values we demonstrate that the predictions of the Kramers theorem for the gyration radius of branched polymers are valid also for the branched droplets' chains. We discuss physical interactions that explain both the high value of the power exponent and the applicability of the Kramers theorem including the effects of the excluded volume, surrounding droplet monomers, and the prohibition of extreme values of the bond angle.

UR - http://www.scopus.com/inward/record.url?scp=85131311207&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.105.055104

DO - 10.1103/PhysRevE.105.055104

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AN - SCOPUS:85131311207

SN - 2470-0045

VL - 105

JO - Physical Review E

JF - Physical Review E

IS - 5

M1 - 055104

ER -