TY - JOUR

T1 - Different measures for characterizing the motion of molecules along a temperature gradient

AU - Farago, Oded

N1 - Funding Information:
I thank Daan Frenkel for numerous insightful discussions and comments on the topic. This work was supported by the Israel Science Foundation (ISF) through Grant No. 991/17.
Publisher Copyright:
© 2019 American Physical Society.

PY - 2019/6/5

Y1 - 2019/6/5

N2 - We study the motion of a Brownian particle in a medium with inhomogeneous temperature. In the overdamped regime of low Reynolds numbers, the probability distribution function (PDF) of the particle is obtained from the van Kampen diffusion equation [J. Phys. Chem. Solids 49, 673 (1988)JPCSAW0022-369710.1016/0022-3697(88)90199-0]. The thermophoretic behavior is commonly described by the Soret coefficient, a parameter that can be calculated from the steady-state PDF. Motivated by recent advances in experimental methods for observing and analyzing single nanoparticle trajectories, we here consider the time-dependent van Kampen equation from which the temporal evolution of the PDF of individual particles can be derived. We analytically calculate the PDF describing dynamics driven by a generalized thermophoretic force. Single-particle statistics are characterized by measures such as the mean displacement (drift) and the probability difference between moving along and against the temperature gradient (bias). We demonstrate that these quantities do not necessarily have the same sign as the Soret coefficient, which causes ambiguity in the distinction between thermophilic and thermophobic response (i.e., migration in and against the direction of the temperature gradient). The different factors determining the thermophoretic response and their influence on each measure are discussed.

AB - We study the motion of a Brownian particle in a medium with inhomogeneous temperature. In the overdamped regime of low Reynolds numbers, the probability distribution function (PDF) of the particle is obtained from the van Kampen diffusion equation [J. Phys. Chem. Solids 49, 673 (1988)JPCSAW0022-369710.1016/0022-3697(88)90199-0]. The thermophoretic behavior is commonly described by the Soret coefficient, a parameter that can be calculated from the steady-state PDF. Motivated by recent advances in experimental methods for observing and analyzing single nanoparticle trajectories, we here consider the time-dependent van Kampen equation from which the temporal evolution of the PDF of individual particles can be derived. We analytically calculate the PDF describing dynamics driven by a generalized thermophoretic force. Single-particle statistics are characterized by measures such as the mean displacement (drift) and the probability difference between moving along and against the temperature gradient (bias). We demonstrate that these quantities do not necessarily have the same sign as the Soret coefficient, which causes ambiguity in the distinction between thermophilic and thermophobic response (i.e., migration in and against the direction of the temperature gradient). The different factors determining the thermophoretic response and their influence on each measure are discussed.

UR - http://www.scopus.com/inward/record.url?scp=85067343508&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.99.062108

DO - 10.1103/PhysRevE.99.062108

M3 - Article

AN - SCOPUS:85067343508

VL - 99

JO - Physical Review E

JF - Physical Review E

SN - 2470-0045

IS - 6

M1 - 062108

ER -