The rate of electron transfer between a molecular species and a metal, each at a different local temperature, is examined theoretically through the implementation of a bithermal (characterized by two temperatures) Marcus formalism. Expressions for the rate constant and the electronic contribution to a heat transfer mechanism which is induced by the temperature gradient between a molecule and metal are constructed. The system of coupled dynamical equations describing the electronic and thermal currents are derived and examined over diverse ranges of reaction geometries and temperature gradients. It is shown that electron transfer across the molecule-metal interface is associated with heat transfer and that the electron exchange between metal and molecule makes a distinct contribution to the interfacial heat conduction even when the net electronic current vanishes.
REFERENCES
1.
A.
Aviram
and M. A.
Ratner
, Chem. Phys. Lett.
29
, 277
(1974
).2.
R. L.
Carroll
and C. B.
Gorman
, Angew. Chem., Ind. Ed.
41
, 4378
(2002
).3.
A.
Nitzan
and M. A.
Ratner
, Science
300
, 1384
(2003
).4.
V.
Coropceanu
, J.
Cornil
, D. A.
da Silva Filho
, Y.
Olivier
, R.
Silbey
, and J.-L.
Brédas
, Chem. Rev.
107
, 926
(2007
).5.
M.
Galperin
, M. A.
Ratner
, and A.
Nitzan
, J. Phys.: Condens. Matter
19
, 103201
(2007
).6.
Y.
Dubi
and M.
Di Ventra
, Rev. Mod. Phys.
83
, 131
(2011
).7.
M.
Galperin
, A.
Nitzan
, and M. A.
Ratner
, Phys. Rev. B
75
, 155312
(2007
).8.
M.
Galperin
, K.
Saito
, A. V.
Balatsky
, and A.
Nitzan
, Phys. Rev. B
80
, 115427
(2009
).9.
M.
Galperin
and A.
Nitzan
, J. Phys. Chem. Lett.
2
, 2110
(2011
).10.
M.
Galperin
and A.
Nitzan
, Phys. Rev. B
84
, 195325
(2011
).11.
A. P.
Horsfield
, D. R.
Bowler
, H.
Ness
, C. G.
Sánchez
, T. N.
Todorov
, and A. J.
Fisher
, Rep. Prog. Phys.
69
, 1195
(2006
).12.
R.
D’Agosta
and M. D.
Ventra
, J. Phys.: Condens. Matter
20
, 374102
(2008
).13.
Y.
Asai
, Phys. Rev. B
84
, 085436
(2011
).14.
Y.
Asai
, Phys. Rev. B
91
, 161402
(2015
).15.
R.
Lake
and S.
Datta
, Phys. Rev. B
46
, 4757
(1992
).16.
R.
Härtle
and M.
Thoss
, Phys. Rev. B
83
, 115414
(2011
).17.
J.-T.
Lu
, H.
Zhou
, J.-W.
Jiang
, and J.-S.
Wang
, AIP Adv.
5
, 053204
(2015
).18.
D. G.
Cahill
, K.
Goodson
, and A.
Majumdar
, J. Heat Transfer
124
, 223
(2002
).19.
D. G.
Cahill
, W. K.
Ford
, K. E.
Goodson
, G. D.
Mahan
, A.
Majumdar
, H. J.
Maris
, R.
Merlin
, and S. R.
Phillpot
, J. Appl. Phys.
93
, 793
(2003
).20.
D. M.
Leitner
, Annu. Rev. Phys. Chem.
59
, 233
(2008
).21.
D. M.
Leitner
, J. Phys. Chem. B
117
, 12820
(2013
).22.
D. M.
Leitner
, Adv. Phys.
64
, 445
(2015
).23.
N.
Li
, J.
Ren
, L.
Wang
, G.
Zhang
, P.
Hänggi
, and B.
Li
, Rev. Mod. Phys.
84
, 1045
(2012
).24.
A.
Dhar
, Adv. Phys.
57
, 457
(2008
).25.
T.
Luo
and G.
Chen
, Phys. Chem. Chem. Phys.
15
, 3389
(2013
).26.
N. I.
Rubtsova
, L. N.
Qasim
, A. A.
Kurnosov
, A. L.
Burin
, and I. V.
Rubtsov
, Acc. Chem. Res.
48
, 2547
(2015
).27.
N. I.
Rubtsova
, C. M.
Nyby
, H.
Zhang
, B.
Zhang
, X.
Zhou
, J.
Jayawickramarajah
, A. L.
Burin
, and I. V.
Rubtsov
, J. Chem. Phys.
142
, 212412
(2015
).28.
Y.-C.
Chen
, M.
Zwolak
, and M.
Di Ventra
, Nano Lett.
3
, 1691
(2003
).29.
A.
Pecchia
, G.
Romano
, and A.
Di Carlo
, Phys. Rev. B
75
, 035401
(2007
).30.
N.
Yang
, X.
Xu
, G.
Zhang
, and B.
Li
, AIP Adv.
2
, 041410
(2012
).31.
N. A.
Zimbovskaya
, J. Phys.: Condens. Matter
28
, 183002
(2016
).32.
B.
Li
, L.
Wang
, and G.
Casati
, Phys. Rev. Lett.
93
, 184301
(2004
).33.
D.
Segal
and A.
Nitzan
, J. Chem. Phys.
122
, 194704
(2005
).34.
C. W.
Chang
, D.
Okawa
, A.
Majumdar
, and A.
Zettl
, Science
314
, 1121
(2006
).35.
D.
Segal
, Phys. Rev. Lett.
100
, 105901
(2008
).36.
L.-A.
Wu
and D.
Segal
, Phys. Rev. Lett.
102
, 095503
(2009
).37.
W.-R.
Zhong
, P.
Yang
, B.-Q.
Ai
, Z.-G.
Shao
, and B.
Hu
, Phys. Rev. E
79
, 050103
(2009
).38.
J.
Ren
and J.-X.
Zhu
, Phys. Rev. B
87
, 241412
(2013
).39.
Y.
Ming
, H.-M.
Li
, and Z.-J.
Ding
, Phys. Rev. E
93
, 032127
(2016
).40.
L.
Arrachea
, N.
Bode
, and F.
von Oppen
, Phys. Rev. B
90
, 125450
(2014
).41.
Q.
Li
, I.
Duchemin
, S.
Xiong
, G. C.
Solomon
, and D.
Donadio
, J. Phys. Chem. C
119
, 24636
(2015
).42.
M.
Delor
, P. A.
Scattergood
, I. V.
Sazanovich
, A. W.
Parker
, G. M.
Greetham
, A. J. H. M.
Meijer
, M.
Towrie
, and J. A.
Weinstein
, Science
346
, 1492
(2014
).43.
A.
Vlc̆ek
, Jr., H.
Kvapilová
, M.
Towrie
, and S.
Zális̆
, Acc. Chem. Res.
48
, 868
(2015
).44.
A. A.
Bakulin
, R.
Lovrincic
, X.
Yu
, O.
Selig
, H. J.
Bakker
, Y. L.
Rezus
, P. K.
Nayak
, A.
Fonari
, V.
Coropceanu
, J.-L.
Brédas
et al., Nat. Commun.
6
, 7880
(2015
).45.
J.
Ren
, J.-X.
Zhu
, J. E.
Gubernatis
, C.
Wang
, and B.
Li
, Phys. Rev. B
85
, 155443
(2012
).46.
K.
Walczak
, Physica B
392
, 173
(2007
).47.
T.
Koch
, J.
Loos
, and H.
Fehske
, Phys. Rev. B
89
, 155133
(2014
).48.
C. A.
Perroni
, D.
Ninno
, and V.
Cataudella
, Phys. Rev. B
90
, 125421
(2014
).49.
N. A.
Zimbovskaya
, J. Phys.: Condens. Matter
26
, 275303
(2014
).50.
A.
Migliore
and A.
Nitzan
, J. Am. Chem. Soc.
135
, 9420
(2013
).51.
R. A.
Marcus
, J. Chem. Phys.
24
, 966
(1956
).52.
R. A.
Marcus
, Annu. Rev. Phys. Chem.
15
, 155
(1964
).53.
R. A.
Marcus
and N.
Sutin
, Biochim. Biophys. Acta, Rev. Bioenerg.
811
, 265
(1985
).54.
R. A.
Marcus
, Rev. Mod. Phys.
65
, 599
(1993
).55.
B.
Peters
, J. Phys. Chem. B
119
, 6349
(2015
).56.
G. T.
Craven
and A.
Nitzan
, Proc. Natl. Acad. Sci. U. S. A.
113
, 9421
(2016
).57.
G. T.
Craven
and A.
Nitzan
, “Electrothermal transistor effect and cyclic electronic currents in multithermal charge transfer networks
” (unpublished).58.
A.
Nitzan
, Chemical Dynamics in Condensed Phases: Relaxation, Transfer and Reactions in Condensed Molecular Systems
(Oxford University Press
, 2006
).59.
R. A.
Marcus
, J. Chem. Phys.
43
, 679
(1965
).60.
J.
Stähler
, M.
Meyer
, X. Y.
Zhu
, U.
Bovensiepen
, and M.
Wolf
, New J. Phys.
9
, 394
(2007
).61.
Y.
Zeng
, R. B.
Smith
, P.
Bai
, and M. Z.
Bazant
, J. Electroanal. Chem.
735
, 77
(2014
).62.
L.
Zanetti-Polzi
and S.
Corni
, Phys. Chem. Chem. Phys.
18
, 10538
(2016
).63.
J. T.
Hupp
and M. J.
Weaver
, J. Phys. Chem.
88
, 6128
(1984
).64.
E.
Laborda
, M. C.
Henstridge
, and R. G.
Compton
, J. Electroanal. Chem.
667
, 48
(2012
).65.
E.
Laborda
, M. C.
Henstridge
, C.
Batchelor-McAuley
, and R. G.
Compton
, Chem. Soc. Rev.
42
, 4894
(2013
).66.
N.
Hush
, Electrochim. Acta
13
, 1005
(1968
).67.
C. E. D.
Chidsey
, Science
251
, 919
(1991
).68.
A.
Migliore
and A.
Nitzan
, ACS Nano
5
, 6669
(2011
).69.
A.
Migliore
, P.
Schiff
, and A.
Nitzan
, Phys. Chem. Chem. Phys.
14
, 13746
(2012
).70.
P.
Reddy
, S.-Y.
Jang
, R. A.
Segalman
, and A.
Majumdar
, Science
315
, 1568
(2007
).71.
M.
Galperin
, A.
Nitzan
, and M. A.
Ratner
, Mol. Phys.
106
, 397
(2008
).72.
S.-H.
Ke
, W.
Yang
, S.
Curtarolo
, and H. U.
Baranger
, Nano Lett.
9
, 1011
(2009
).73.
Y.-S.
Liu
and Y.-C.
Chen
, Phys. Rev. B
79
, 193101
(2009
).74.
S.
Sadat
, A.
Tan
, Y. J.
Chua
, and P.
Reddy
, Nano Lett.
10
, 2613
(2010
).75.
A.
Tan
, J.
Balachandran
, S.
Sadat
, V.
Gavini
, B. D.
Dunietz
, S.-Y.
Jang
, and P.
Reddy
, J. Am. Chem. Soc.
133
, 8838
(2011
).76.
Y.
Kim
, W.
Jeong
, K.
Kim
, W.
Lee
, and P.
Reddy
, Nat. Nanotech.
9
, 881
(2014
).77.
E.-S.
Lee
, S.
Cho
, H.-K.
Lyeo
, and Y.-H.
Kim
, Phys. Rev. Lett.
112
, 136601
(2014
).78.
J.
Koch
, F.
von Oppen
, Y.
Oreg
, and E.
Sela
, Phys. Rev. B
70
, 195107
(2004
).79.
L.
Simine
, W. J.
Chen
, and D.
Segal
, J. Phys. Chem. C
119
, 12097
(2015
).80.
It is important to note that these results depend on the protocol used to define and . We will expand on this issue in a future paper.
© 2017 Author(s).
2017
Author(s)
You do not currently have access to this content.
