Subscriber access provided by University of Washington | Libraries
Article
Stochastic Kinetics on Networks: When Slow is Fast Xin Li, Anatoly B. Kolomeisky, and Angelo Valleriani J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/jp506668a • Publication Date (Web): 20 Aug 2014 Downloaded from http://pubs.acs.org on August 26, 2014
Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.
The Journal of Physical Chemistry B is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.
Page 1 of 30
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
The Journal of Physical Chemistry
! #"$% & ' (*),+-.)0/2143+65879;:=@?BAC9;:D9;E%F6)HGJIK PU:6#V !: & @)W&8>&/ "/%;#%$ ( & Xm¬Rw$;x(pûÈw$r
ü zRqsm{tOv7m
xs=¥'m=n$zR
8w$Jim?
p'v*x(mrJn
m8w$*tAp$^tOx(w$*rRw6qsrWxsm{
y**=¬*m{t ¯ ¯¨ ¯ ¾ ª>y*mw$Rw$VnxsZ
{w$m v*qsmtstOZp'L¢p'q3x(y*mTv*qsp$Rw$*=Z=x n
=< û ?û >A@ D @ û4>B@ C ,< =< û û8>B@
7:9
À0í
Éé
À
@
07%9:tsy*poN·Z´à,Z~
tOntx(m{âqOm8w$
y*mtGxsy*m)|RRw$.txw6xsmGßx(yqsp'*~$y·vRw]x(y/oPw8n
Á{À
Á
´x(yRw]xXx(ym
û
À Á ê
w$*rËí,zGoNy*m{qOm¼xsy*mÄvRw$qsw$Ymx(mq
@FE G
Î $òÉw$*rËx(ym
yp'Zr*t ¶ *m3
8w6dqsm{w$r*==ntOm{m3x(yRw6xEw$tEòK~'qOp oNtXÀ¢xsy*m`vRw$qsw$Ymx(mq
Äé
I7:9
im{
p'm{ttsYw$Z=m{q(Á?x(y*mJv*qOp'Rw$ZZVx n
Mxsp¼qOm8w$
yÍx(pax(ymJ|*Rw$>tOx(w6x(mß¿xsy*qsp$*~'y¸x(y*mJ
yRw6Z
²
im{
{p$YmtcZw$qs~'mqw$*r«w$v*v*qOp/w$
y*mtd**Vx n'L¤\x?
{w$«imYvqsp¥'mr«x(yRw]x?xsy*Ztv*qOp'Rw$ZZVx n¢*
x(=p'¼Zt?w r*m
{qsm{w$ts=*~¢**
xsZp'´p$
@
p$
@
zw$tNr*m{p'*tx(qsw6x(mrZ´à,=~*
7%9
`ª>y*mcrm{qsV¥6w6x(V¥'mp$
µoNVx(yHx(ymcqOm{tsvim{
x
{w$·im)oNqsVxsx(m´w$t
J 7:9 J@
=< û LK < @ DC > +< û @ DC >TûLM K @ û8>A@ %C ,< =< û û8B> @ M
À0í é
Á VÀ0å
ó
À
=NPNTORSVQ UXW
¶ *m
8w$´m8w6tsZVnLtOy*poþx(y*w6x
ó
Á
À0å
Á þÀ¢í
ó
Á
ÁÀ
¯
Á ¯
À Á ë
im{
{w$*tOm?oAmcy*w¥$m
%< û YK Z< @ %C > Z< û @ %C ~> ûLM D< û û[>@ LK Z< û @ DC > û < @ < < @ M UXW
À0í
Á =À¢å
Á
ó
À¢å
Á
ó
¯
ékÀ¢í
Á{À
Á VÀ0å
Á
\
ACS Paragon Plus Environment
ó
À
ëVëVë
ó Á
ÀÅ Á
Page 7 of 30
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
The Journal of Physical Chemistry
W^] @ ] û
¢p'q
_7%9
ª>y*m)v*qOp'Rw$*=ZVx n
û
JoNZ=7im
Zp'tOmTx(p
w$tXx(ymvRw$qsw$Ymx(mq
@
w$v*v*qOp/w$
y*mtPx(pKm{qOpw$tPZr*Z
{w6x(mr
Z·à,=~* zRoNy*=
ym8w$*tNx(y*w6xNx(y*m?x(y*m|RRw$^txw6xsm2ßW=tTqOm8w$
ym{rµYw$Z=nx(y*qOp'*~'y´x(y*m?Zp'~'m{qNvRw6xsy ²
=x(ym)
{p'qOqsm{tOv7p$*r*Z~YZmx(=
x(qsw$*tsVx(=p'*tP=Lx(y*=t>vRw6x(y´im{
{p$YmtN0w6tOx(mq{ º p oAm¥$m{qzixsy*mv*Z
x(*qOm
yRw$~'m{tNq(w6r*Z
{w$ZVnoNym{JoXm)
p'*ts=r*m{q>xsy*m)
{p'/xsqsZx(=p'*tX¢p'qAx(y*m)qOm8w$=Z8w]x(Zp$Lp$^x(y*m)vqsp
{m{tOt>¢qsp'
x(ymx oApvRw6x(y/oXw8n tG¢p'qP¥6w$qs=m{rJvim{qs=p rt>p$ExsZm$
` ab c#3d. [$ )ef-gih: $Tjkl ( )/ f,-/.01 ). % 5 , 64 ª>y*m[|RqOtOxO}\vRw$tOt(w$~'m`x(=Ym9w$v*v*qOp/w$
y 0½¨°0¾ Zt^w>vipoXmqO¢*'xsp p'6x(pNZ/¥'mtOxsZ~/w6xsm[x(y*m9xsm{v7p'qsw$'m¥'p'=x(=p')p$
1mn9 omp;
Yw$/n)
y*m{Z
{w$w$*r?*Zp$Zp'~'=
8w$6tOntOxsm{t{ º m{qOm$z]oXmAr*m|RmA¥6w$qsZw$*=m{t
w$*r
Lw$t^x(ymA
p'*r*Vx(Zp$Rw$
q(w6*r*p'xsZm{txsp·qOm8w$
y¼x(y*mQ|RRw6[tOxw]x(mcß´¢qsp$x(y*mZ=x(Zw$tOxw]x(m Þ oNy*m{¼x(y*mfw$tx)¥ZtsVx(mr¿txw6xsm v*qOZp'qxspYß·Ztx(ymtxw6xsm æ/ó
qmp;
w$*r
emp9
w6*r«ï(õ z^qsm{tOv7m
xs=¥'m=n$Yª>y*m*p'qOWw6ZZm{rÄv*qOp'Rw$ZZVx nrm{*tO=x(=m{tp$
=r9 =rn;
´oN=Z7mXr*m{*p6x(m{roN=xsy
Ww$*r
[z'qOm{tOv7m
x(V¥'m=n'[ª>ym{tsmNr*m*tsVx(=m{t9
{w$7m>
p'Yvx(mrQ*ts=*~
x(ymdx(m
y**Z¬*mdp$[x(y*mKw$*tsp$qsvxsZp'´x(Zm{tTm v*Zw$Z*mrµZ·v*qsm¥Zp'*t2tOx(r*Zmt{§¯ ¯(¨ ± ®à,ZqOtOxs=n'zRoAmQr*ZtO
{*tOt x(ym)w8¥'m{qsw$~'m)
p'*r*Vx(Zp$Rw$iw$*tOp'qsvxsZp'Yx(ZmTw$Zp'~cx(ym)
{p'v7mx(=*~dvRw]x(y/oPw8nt>oNy*Z
yJw6qsmr*m|R*mr·w6t
s mnt?u w v rzt yx x x Wé
{
¢p'q éÉû êü
s mp9pu
[ª>y*m
Pw$*r
À ÁPr
ÀÕ Á ê
®
s mp;ku
Xr*m{tO
{qOZimx(y*mw8¥'mq(w$~$mx(Zm{t3x(yRw]xN=xXx(w$$mtP¢p'qXxsy*m)tOntOxsm{÷xsp
qsm{w$
y·xsy*m|RRw$^tOx(w6x(m¢qsp$÷x(y*m?
{p$YvimxsZ*~vRw6xsy/oPw8nt{Nª>y*m?ZmtstNx(Zm)=xN
p'*tO*Ymt{zx(y*m0w$tx(m{qG=x Zt[¢p'q[xsy*mTtntOx(m×xspcqOm8w$
yYx(y*mN|RRw$Rtxw6xsmGxsy*qsp$*~'yYxsy*mGvRw6x(y/oXw8n'Aì ZZZw$q,im{y*w¥=p'qstAw$t`p'x(w$Z*mr
87:9 7D;
¢p'qPxsy*mv*qsp'*w$*Z==xsZm{t
aw$*r
¼
8w$´im?p$*tsmqO¥'mr¢p'qPxsy*m{tOmdw8¥'mq(w$~$mcv*qOp'vim{qOxsZmtGp6Exsy*mtOntOxsm{´
mn9
² t2tsy*poN¼ZÄà,=~* Å zgxsy*mQw8¥'mq(w$~'mK¥6w$=*mKp$ x(ymKx(q(w6*tsVx(Zp$q(w]x(mò¼=µvRw6xsy/oPw8n
²
mp;
«im{
p'm{t)tsYw$=Zm{q>xsyRw$µx(ymw¥$m{qsw$~'mQp$
ÍoNym{
im{
p'Ymtfw6qs~'mq{ª>y*m{qOm¢p'qOm$z;oNy*m¹òaZtZw$qs~$mdm{p'*~'yÄx(ym
|
ACS Paragon Plus Environment
The Journal of Physical Chemistry
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Zp$*~'m{q?vRw6xsy/oPw8n
²
Page 8 of 30
Zt0w$tx(m{qdw$*r¹p'qOmYv*qOp r*
xs=¥'mYx(yRw$¼x(y*mWtsy*p'qx(mqdvRw6xsy/oPw8n«ã2zEp$¸w8¥'m{qsw$~'m6
º poAm¥$m{q{zir*=tOx(=*
xs=¥$m)v*y*m{p'YmRwQoNZZg7m)p'tsm{q¥'mroNy*m{´oXmcw$Rw6*r*p'Hx(ym¥=moÊp6,x(ym?vqsp
{m{tOt Rw$tOm{r·tsp'=m{=nYp'·w8¥'m{qsw$~'m)¥6w$Zm{t{
4m
Ì«mw6Ztspdr*m|Rmx(y*m)qsw$*r*p'
¥6w$qsZw$*=m þw$tXxsy*mx(=YmGx(yRw6xAx(y*m)tntOx(mtsvim{r*tN7m¢p'qsm2¥=ts=xsZ*~
x(ymTtxw6xsmPßc¢p'q`x(ymG|RqOtOx3x(=Ym6ztxw$qx(=*~?¢qOp'kxsy*m2txw6xsm Þ 3ÆV¥'m{x(y*w6xPw?qsm{w$Z=8w6xsZp'Q=m8w8¥Z*~ Þ w6*r qsm{w$
y*=*~Gßxsp p'cmw$
x(=nKw
{mqOxw6ZKx(=Ym
Dm
Sb ye
x
z 0Ç {Ç ~'=¥$m{Qx(y*w6x äé
z'oXm>oAp'*Zr=Z$mAx(p)r*mx(m{qOY=*mPx(ym
x
v*qOp'Rw$*=ZVx n?xsyRw6x[xsy*m>qsm{w$
xsZp'QqOp'x(m>
p'm{t`w$=p'*~x(ym>vRw6x(y/oXw8nã¸oNVx(yQtOZpoXmq`=*mxsZ
t{[ìxw$qx(Z~
_m ] x }
oN=xsyHx(y*m
{p$*r*=xsZp'
w$*rJ*tOZ*~YãPw8n'mtGxsy*m{p$qsm{´zoAmcy*w¥$m?xsyRw6x
2~ m ] x
[q;ú]ùÙé ü
ý
} m ] ~ } m x ] x mp; `q;ú
é
[q{ú
Tp6x(Z
mN*poÒx(yRw6x3/nx(y*mGr*m|R*=xsZp'p$7x(y*mNx(=Ymt
} Lm ] ~ x `q;ú
ùÙé
ùÙé ý
7%; ë
À ÿ Á
~'V¥'mWm8w6qsZ=m{qz/Zx(y*mGqsy*tAp$`À ÿ Á,oXm2w$ZtOpcy*w¥$m
E } m1; ] x [q;ú
üYý
üYý
w rn;
é
ý
r
`À RÁ ê
\
À Á
®
oNy*mqsm8w6tG¢p'qPxsy*mr*m{p'Y=Rw6xsp'qXoAmcyRw8¥$m
} m ] x [qú
=r
ý
w $r é
r
r g7:9pr9
k|*Rw$ZVnW=m8w$rtPx(p
À 'Á
Tp6x(Z
m2x(y*w6xPx(yZtPm¬*w6x(=p'HZtX¥$m{qnH~'m{m{q(w6;w$t>VxPqsm¬*ZqOm{t>p'*VnYxsyRw6x>=JwKqsm{w$
xsZp'Lmx oAp'qsWxsy*m{qOm
ACS Paragon Plus Environment
Page 9 of 30
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
The Journal of Physical Chemistry
b
m =tOx(twWvRw6xsyoXw8nÄãÊw6*rÄw6x2Zm8w6tOx)w6*p$x(ym{q2
p'v7mx(Z~WvRw6xsy/oPw8n' GpW¢*qx(y*mq)w$tstO*vx(=p'*t2y*w¥$m
%
im{m{Yw$r*mPp'Qxsy*mNq(w6xsm{t[p'q[p'Qxsy*m>tOxsqs*
x(*qOmGp67xsy*m>*mx oAp'qOQZQp'qOr*m{q9xsp?rm{qsV¥'mN=x{ Gm¥$m{qOxsy*m{=m{tOt{z oNy*mËoAmÄ¢p
*tLp'Mxsy*mÄ*mx oXp'qOMtsyp oNäZMà,Z~*
û
!
w$*rÒp$Ëxsy*mµ
y*p$Z
{mÄp6?xsy*mµvRw6q(w$mxsm{qstJw6t
r*mts
{qOZim{r¿w$ip ¥$m$z.oAmY
{w$am8w$tOZ=nqsm{w$Z={mdxsyRw6x [¬3À /Á2
{w$a7m*p'} p'*p$xsp'*Z
dw$t¢**
x(=p'ap$ ¤ *r*mm{r;zRw$tOm{r¼p'µx(ymqOm{tO*=xst)p$(¯ ¯z;¢p'qTx(y*m*mx oXp'qOµZ¼à,=~*
rn;
`À ÁXw$t
x
x W
7m
8w$tsm2xsy*mvRw6xsy/oPw8n
w$*ra=t2x(y*tr*m
{qsm{w$ts=*~H¢p'q)Z
{qsm{w$ts=*~
1r9
x(yZt[¢**
x(Zp$
{w$qsZtOmGw$~/w$=Q=
²
û zkr9,À
z x W rn; x x
x
,À Á9r*m{
{w8n tAYp$qsm>q(w6v*Zr*VncxsyRw$
x
x W x
ZtXwcZp$*~'m{qA
yRw$=;9ª>y*t{z [¬.À /Á[m{¬Rw$=tP**Vx nWw]x ZÄx(ymQ*m{=~'y7p'qOy*pp rµp6
x
Á2~'pm{txspH{mqspJ0w$tOxsm{qx(y*w$
é
K·p'qOm{p¥'mq{zEw$t
é
3À Á9=xsy*Zt[=Z=x>ÀUw$mw$v*=m
oNy*mqsm>x(y*=t9yRw$vv7m*t[Zt9rZts
*tstOm{rYZKp'qsmXr*mx(w$Z=t,fw]x(m{q(Á ² x[x(y*mPp'm{/x9oAmP¢p
*t[p'*q`w]xsx(m/x(Zp$
H
w6xxsy*mKqOm{~'=Ymcp$`x(Zm{tT
{=p'tsmdxspH{mqsp*zgoNym{qsm [¬`À /ÁTZt2Yp'p$x(p'Z
8w6Z=nLr*m{
qsm8w6tsZ~Jw$t2¢**
x(=p' p$
[Ì«m)
{w$Zix(y*=tPx(=YmTqsm{~$Zm$z xsy*mqsm~'Zm2p$E*Vx(q(w]0w$tOx>qOm8w$=Z{w6x(=p'*t3p$Exsy*m)v*qOp
m{tstNr*mv*Z
x(mr·=
x û
à,=~*
[¤ Jx(ym¢p$ZZpoN=*~*zoXmcw$qsm)~$p'Z*~Qxsp
y*w$q(w$
x(mqsZm)x(y*=t>qsm{~$Zm)Yp'qOmv*qOm{
{=tsm=n'
ì Z
{mH*Vx(q(w]0w$tOxdv*qsp
{mtstsmtWw6qsmL
qs=xsZ
{w$ZVnaZv7p'qxw$/xKw$*r¹oNZrm{tsvqsm8w6rÂ=¸
y*m{Z
{w$Pw$r¸*Zp6} Zp$~'Z
{w$7tntOx(m·zRoAmdw6qsm)Z/xsm{qsmtOxsm{r=J*=xsq(w60w$tx>qsm{w$Z=8w6xsZp'tAoNy*=
yw$qOm)x(y*p'tOmp
{*qOqsZ~Yw]xNtsYw$Z x(=Ymt
¢p$qPx(y*mtOntx(m{âtOy*poNZ´à,=~*
x
}
[q;ú]ù
û 9Ì«m*tOmLÀ/ÁAx(pr*m|R*mcwQxsZm é
~ m
øé
ü
x
ý
é
x
oNy*=
y´¢*V|RZ=t
À 'Á ê
tsp´x(yRw]x?xsy*mv*qsp'*w$*Z==x n·x(yRw6xxsy*mY
ym{Z
8w63qOm8w$
x(=p'¿y*w$tcp
{
*qsqOm{r¼x(y*qOp'*~'y¼x(y*mvRw6xsyoXw8n¿ãá=t
fw6qs~'mqxsyRw$
Äw$*r
x
m
J=Ax(y*mYqsm{w$Z=8w6xsZp'
yRw$r«r**q(w]x(Zp$¿tOWw$=ZmqxsyRw$
8w$ÍimLp'x(w$Z*mrÍw$Rw$Vnx(Z
{w$ZVnĢqsp'
x(ymÄw$tx(mqWm{¬Rw]x(Zp$Mw$tOtsp
{fw]x(m{rÂx(p¹àEZ~*
x
w6tstsp
{Zw6x(mr¸x(pawµ
{mqOx(w$Z
r Irnx;
À 'Ácp'*
m
Âw$*r
Jª>y*mYqsm{Zw6x(=p'*tOy*Zv¼7mx oXmm{
ËyRw8¥'mJim{mÔ
p'v*x(mr¸¢qsp'
û MÌ¿mtOy*p'*=rÂxsy*m{qOm¢p'qOm*p$xsZ
m$zPx(y*w6xYxsy*m·¥6w$=*mJp$
µw6*r¸x(y*tw$=tspµx(ymHq(w$*~$mLp$Nx(=YmYts
8w6Zm{tw6tstsp
{Zw6x(mr¹x(pÄ*Vx(qsw60w$tOx
qsm{w$Z=8w6xsZp't)Zt?r*m{vim{*rm{/xQp'«xsy*mp ¥$m{qsw$Z3tOxsqs*
x(*qOmLp$Xxsy*mWmx oAp'qs¿w$*r¹p$¿x(ymW
y*p'=
{mYp$Px(ym q(w]x(m
{p'tOxw6xst{
ACS Paragon Plus Environment
The Journal of Physical Chemistry
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
ª>y*m?*fw$
WZZmZ´à,=~* Õ tsy*poNtNx(y*mqOm{fw]x(Zp$*tsy*=vL¢p'qPx(ym?mx oAp'qsH=·àEZ~* tOx(w6x(mt>å ηé
û
é
ÿ zí·é
û
Page 10 of 30
oNVx(yJ*Kim{qNp$
À¢xsy*mtsw$Ymw6tXoPw6t>*tsmr·=Hà,Z~ w$r·àEZ~* Å Ázw$*rHx(qsw$*tO=x(=p'Wqsw6x(mtGòHé Õ
z
À0w$qs*Vx(qsw$qOn**Vx(t(Á ² tXZ*r*=
8w6xsm{rL/nYx(y*mrp$xsxsm{rHZ=*m{tAZHàEZ~* w$*rJàEZ~* Å zx(y*m|R*w$gtxw6xsm
ßHZtYw$=*=nHqOm8w$
ym{rÄ¢qsp' ã2z`ZÔw8¥'mq(w$~$m$
²
xsy*mKZp$*~'m{qTvRw6xsyoXw8n
A
º poAm¥$m{q{zPxsy*m´v*qsp'*w$*Z==x n
oNVx(y0w6tOx(mqq(w]x(m{tTx(yRw$·x(y*mKtOy*p'qx(m{q2vRw6x(y/oXw8n
Äxsp«qOm8w$
yÔx(y*mJ|RRw$Ntxw6xsmWß¿xsy*qsp$*~'yÍx(y*m´tsy*p$qOx(mq
vRw6xsy/oPw8nãþZ*
qsm{w$tsmt)w$tNx(y*mcqsm8w6ZZ{w6x(=p'Jp$[x(ymdv*qOp
m{tst27m
{p'm{tT*=xsq(w60w$txTw$t2tOy*poNÄZµàEZ~* Õ
%
² r´xsy*m¥6w$Z*m)p6 doN=Z77m)Zw$qs~'mqXx(y*w$Jp'*myRw$V,w6tPx(Zm
x
7m
{p'm{t>tOWw6ZZmqAoNy*=
y·m8w6*tPx(yRw]x
x(ymctOy*p'qOxsm{qNvRw6xsy/oPw8n·ãËoN=Z;rp'Y=Rw6xsm2x(y*m?qsm{w$Z=8w6xsZp'Wp$,xsy*mv*qsp
{mtst2im{=poþx(y*w6x>x(=Ym6 ² xGx(ym Z=YVx(=*~)
8w$tOm)w$t3x(Zm
x
w$v*v*qOp/w$
y*mtP{mqsp*zw$Zp$.xsy*m2
y*mY=
8w$iqsm{w$
xsZp'tAoNZ=p
{*qAp'*=nxsy*qsp'~'y
x(ym?v*w6x(y/oXwn´ãTz*oNy*Z
y´~'=¥$m{tNts=poXmqG=*mxsZ
{tN* xT
p'/xw$=*t>ZmtstN*Kim{qNp$,Z/x(mqsm{r*Zw6x(mtxw6xsm{t ª>y*=tZt2wL**=¥$m{qOt(w$Ev*y*m{p'Ym*p'Äx(y*w6x=t2m vim{
x(m{rax(pW7mKp$*tsmqO¥'mr¿qOm{~/w6qsr*=m{tst2p$`x(y*md¥6w$=*m{tTp$ x(ymdZ*mx(=
cvRw6q(w$mxsm{qstG¢p'qTw$Z^*mx oXp'qOt{ º p oAm¥$m{qz;x(y*=tT=t2wWtO*qsvqsZtOZ*~Yqsmts*VxTxsyRw6x
{w$**p6xim **rm{qstx(pp rJ¢qsp$x(ym?rZts
*tstOZp'´p$,w8¥'m{qsw$~'m?v*qsp$v7mqOx(=m{t>p$x(ym?tntOx(m·
Ì«mctsy*p$*Zr·tOx(qOm{tOtw$~/w$=´xsyRw6xT7p$xsy
Zr*m{vim{*rm{/x(Vnp$,x(y*mKmw$YvZm?tOx(r*ZmrÄZµàEZ~*
8w6tsm~'=¥$m{¼Z¼à,Z~
û
û
[¬9À /ÁNw$*r
[¬9À /ÁNw$qsm?¥'m{qn~$m{*mq(w$qsmts*Vx(tTxsyRw6xTy*p'=r
Tm¥'m{qx(y*mZmtst{z;oAmQyRw8¥'md
y*p'tsmÄx(pWtx(*r nx(ym
ÀUw$*r¿wJtsZv*=md¥6w$qsZw$/xp$XVxr*ZtO
{*tOtsmr¹fw6xsm{q)=axsy*mWw6ts
{qOZvxÁ7m
8w$*tOm
oAm7mZ=m¥'mTx(yRw6xAx(y*=tXm*w6Yv*=m2=tAx(ymYp$tOxP=*tOxsqs*
x(V¥'mp'm2ts=*
{m2=xPyZ~'y*=Z~'y/xst`xsy*m
p'/x(q(w6r*Z
x(Zp$ imx oAm{m{Â7mZ*~·0w$tOx=¸w8¥'m{qsw$~'m´w$*r¸im{=*~Äqsmtsvip'*tOZ*=mW¢p'qdxsy*mH*=xsq(w60w6tOxQqOm8w$=Z8w]x(Zp$*t{Ĥ ¸x(ym
{p$xsmx[p$Rà,Z~*
Z
Z
û
z o
w$*rd¢p$q¥6w$=*m{tp$ NvRw$qx(Z
*fw6qs=nfw$qO~'m$z]=xZtvip'tstOZ*=m3xsyRw6xx(y*mAm¥'m/x(t[
{p$*ts=r*m{qOm{r
[¬`À /Áw$qsmdvRw$qOxsZ
*fw$qO=n´q(w6qsm$ ^w6x(mq)p'µoAmtOy*poz^y*poXm¥'m{qzxsyRw6x)m¥'m«=`qsw$qsmKxsy*m{tOmm¥'m/x(t
w$qOmXoXmZRw67p¥'m>xsy*mPr*mx(m{
x(=p'
8w$vRw6
{=x ndp$iYpr*mqsQm vim{qOZm{/xw$x(m
y**Z¬*mt3¢p$q,x nv*Z
{w$
{w6xw$Vnx(Z
qsm{w$
xsZp't{
ûW
ACS Paragon Plus Environment
Page 11 of 30
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
The Journal of Physical Chemistry
.. k-g %$&1. $j(el & kj % j $. 01 5 k¢¡ h¤£L¥ àRp'qdp'qOmWqsm{w$Z=tOxsZ
Yw$v*v*=Z
8w]x(Zp$«=xdWw8n¿7mW*tsm¢*Xx(pp'xw6Z¸w$Íw6v*v*qsp8 ZYw6xsmWm v*qOm{tOtsZp$Ôp6
û ÁzXxsy*m{Âx(y*m·qsm{Zw6x(=p'Ô7mx oXmm{Mx(ym{tsm·x oXp«¥6w$qOfw$Zm{t
{w$Mixm
¦
oNy*m
¼=tYZw$qs~'m¿À0w$v*v*qOp/w$
y*mtWx(p
p'*tOm{q¥'m{rar*=qsm
x(Vn'2ì Z
{mcoAmQw$=âw6x)w6Rw$=nZ*~x(y*mc7myRw8¥ =p'q2p69x(y*mdtOntOxsm{w]x2m{w$qsVn´xsZm{tzioAm
ÓO*txQ*m{mr¹x(pµ
{w$Z
*fw]x(mx(y*mLrm{*tO=x(=m{tcZËÀ /Á¢p'qctsYw$Z[¥6w$=*m{tcp$
x
µ¤ ¹vRw6qOx(=
{*Zw$q{zoXmW
8w$¸*tOm
x(ymcqOm{ts=x(tGr*m¥'m{=p'vim{rµqOm{
{m/x(=nJ= ¯s ¨ ¯ ¯ w$*r·m vRw$*r¸À /Á>w6xGtsYw$=;x(Zm{tA¤ r*m{mr;zg*tOZ*~*poîx(ym ~'qsw$v*yHx(y*mp'qsmx(=
8w$^w$vv*qsp/w6
y;z§¯ ¯ToAm)|R*r·xsyRw6x
rn; ¢7b; § ¨ C %© y*m>t(w6Ym>w6v*v*qsp'w$
y
x
û¾û Á À
ê
oNy*mqsm
3À Á)Ztx(y*mYt(w$mYvip'Vn p'YZw$9w6tdim¢p'qOmWw$r«pÀ ó Áw$qsmx(mqstcp6>p'qsrm{q?fw$qO~'m{q)x(y*w$¹å
oNy*m
w6v*v*qsp'w$
y*m{td{m{qOp*aì *tOxs=x( x(Z~ÍÀ
x
x
z
,À Á`
8w$Himmv*w$*r*mr·w6t
¬ ¨ C %x © x(pwK|RqOtOxGp'qsrm{qGw$v*v*qOp8=Ww]x(Zp$LZ
®³ ¯ û ¨ û8> :© © @ C ¬ ±² § x =° ò
oNy*mqsm
@´E G
Î $òÂw$*r
¯ x
À
$Á
å
õ
í
õ
ó
=tw$Ôw$v*v*qOp =Ww6xsmHm v*qOm{tstOZp'Ô¢p'q
x %ª®;
û
À Á ê
r*m|R*mrÃZÉÀ /ÁKw6xtsYw$=Ax(=Ymt{
Tp6x(Z
m2x(y*w6xPx(yZtPqOm{ts=xPoN=Zir*m{vim{*r´p'*Vnp'Hx(y*m2¢p$qOoXw$qsrJq(w]x(m{tPw$Zp'~dx(y*mx oApvRw6xsyoXw8nt ² ã¸7m
8w$tsmGw$ZRw$
/oXw$qsrYq(w6xsm{t[
{w$p'*=ndw$v*vim8w6q[w6x[x(ymPx(m{qOYt
w6*r
w6*rQpÀ ó Á,w$t[rZts
*tstOm{rYZQ»Nm¢t
û¾û
ACS Paragon Plus Environment
x
The Journal of Physical Chemistry
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
¯ x
¯s&¨ ¯ ¯[àRqsp'îxsy*mPm v*qOm{tOtsZp$Yw67p¥'m6z'oXmX
8w$Qp' xw$=Kr*ZqOm{
x(=n)xsyRw6x
Page 12 of 30
Zt,w$=oXw8nt[w2r*m
{qsm{w$ts=*~¢**
x(=p'
p$ G~'=¥$m{QåöÂíHw$tEp'*tsmqO¥$m{rZQàEZ~* Õ qOm{~/w$qOr*ZmtstEp$Rx(y*mAx(q(w6*tsVx(Zp$cqsw6x(mt`òw6*rKÎ9Eª>y*m{qOm¢p'qOm$z/=x Zt`w~$m{*mq(w$RqOm{fw]x(Zp$Qw$t[r*=ts
{tstsmrLw$ip¥'m>x(y*w6x9x(ymGtOy*p'qx(m{q[v*w6x(y/oXwnã¹oN=Zrp'Y=Rw6xsmAx(ymGvqsp
{m{tOt
_
¢p'q>x(ymctn tx(mâxspYqOm8w$
y·x(y*m|RRw$.txw6xsm2ßHw]xTtOWw6ZgxsZm{tNw$*r´x(y*m?
{p$qsqsmtsvip'*r*=*~v*qsp'*w$*Z==x n
û
x(yqsp'*~$yaxsy*Zt)v*w6x(yam¥$m{¿qsm8w6
y*m{tx(p
8w6µw$=tspp'*tsmqO¥$mcx(y*w6x
¯ x
w$txsZmK7m
{p'm{t
Zp'tOmKx(pJ{mqsp*QàRqOp'øxsy*ZtqOm{Zw6x(=p';zgoAm ²
oN=Z.im{
p'YmtOWw$=ZmqNw$tGxsy*m¢p'qOoXw$qsr·q(w6xsmcòÄ=´xsy*m?Zp'*~$m{qNvRw6xsyoXw8n
Z
{qsm{w$tsmt)p'q2xsy*mK¢p'qOoXw$qOrÄq(w6xsmKθZxsy*mQtsyp'qOxsm{q)vRw6xsy/oPw8naãÊr*m
{qOm8w$tOm{t{cª>y*m{qOm¢p'qOm$z.oAmQ*m{mraxsp r*mx(m{
xcxsy*mQv*qOp
m{tstcw6x*Vx(qsw60w$tOxp$q)tsYw$Z=m{qTxsZmKqsm~'ZmKVAoAmQoPw$/x?x(pJp'*tOm{q¥'mx(y*mtOntx(m{xsp qsm{w$
yHx(y*m|*Rw$gtxw6xsmNßYw$=*=nx(yqsp'*~$yLx(y*m)tOy*p'qOxsm{q>vRw]x(y/oPw8nJãÒw6tPx(q(w6*tsVx(Zp$WZ*mx(=
{tPim{
p'Ymt 0w$tx(m{q9¢p$q[Zp'*~$m{q9vRw]x(y/oPw8n ² v*=p$xp$
¯ x
p'q[tOZpoAm{q[¢p'q9x(ym>vRw6x(y/oXw8nãÍVx(tOm{=&E¤ à,Z~* Õ x(y*m>qOm{rZZmP~'=¥$m{t[x(ym
z
w$t9wN¢**
x(Zp$dp$ Gw$*rc=xEZt
{p'vRw$qOm{r?oN=x(y?x(y*m3mw$
x[tsp$ZxsZp'
x 8
r*m{qO=¥'mrKm8w6qsZ=m{qz oNyZ
y
ZtGZr*Z
{w6x(mr·/nJx(y*mc*fw6
HZZm$P¤\xTZtG
{=m8w$q>x(y*w6xw]x2Zw$qs~'m)¥6w$=*m{tGp$ ·À0
Zp'tOm?xsp vim{qO¢m
xGm{tx(=Ww6xsm)p$ ²
x
oNy*Z=m
~'m{*mq(w$Nmvqsm{tOts=p'¢p'q
¯ x ¯ x
Zt>tn tx(mWw6xsZ
{w$ZVnWtOWw$=ZmqXx(yRw6
û Áz ¯
x
v*qOp¥ =r*m{t2w
x
w6t im{
p'm{tNtsYw$Z=m{q
{w$Ãw6ZtspaimJp'xw6Z*mrÔ¢p'qKxsy*mHx oXp¿vRw6xsyoXw8ntYoN=xsyÃw6qs*Vx(q(w6qOn
x(qsw$*tO=x(=p'´q(w6xsm{t2/n·*ts=*~Yxsy*mKmv*w$*ts=p'xsm{
y**=¬*md¢qsp$· ¯ ¯ Æ)=¥$m{´x(y*m?¢p'qOoXw$qsrq(w6xsm{t)ò ç zoN=xsy èé
û'ê8ë{ë8ë{ê å
ZHxsy*mvRw6x(y/oXw8n
²
w6*r·Îðz*oNVx(y
³ ± ² § p µ © ¯ ¨ û8> %© µ n¶¶¶ ¬ p¶¶ ¶ x"° À
pµ
µ
û$ê8ë8ë8ëê íÄZHx(ym?v*w6x(y/oXwn´ãTzR=xNZm{w$r*tPxsp
ñ é
'Á
Î fÎ
å
í
ò ¢ò
Îgõ
ó
ò ó
õ
û
À Å Á ê
oNy*mqsmHÎ Pw$*rÍò >w$qOmWx(ymY¢p'qoPw$qOr¸q(w6xsm{tdw$tstOp
fw6xsm{r¹oN=xsy¿xsy*mLtOx(w6x(m Þ Z¹à,Z~*
û
û ·ª>y*Ztd~'m{*mq(w$
[·
m v*qOm{tOtsZp$KZt^¬*=xsmAtOZZZw$q7xspKÀ Áz6w$*r?x(y*m3
{p$*
{=*ts=p'*tp'xw6Z*mrcv*qOm¥Zp$*tsVn?w$qsm`*p$xEZ R*m{
{m{rg ¤\xGw$=tspKtOy*poNtNxsyRw6xPxsy*m)*poNZmr*~'mp$p'*VnYxsy*m¢p'qOoXw$qOrHq(w6xsm{t>ZtAx(y*mqsm¢p$qsm)ts ÐY
ZmxNxspQm{tOxsZYw6x(m x(ymPx(ZmXtO
8w$=m
x
,ª>y*=t[tsy*p'Zrw$=Zpo¸*t`w$m{w$tOncoPw8ndxsp¥'mqs=§ncx(y*mp'qsmx(=
8w$ v*qsmr*Z
x(Zp$*t9/nKm8w$t
p$7ts=*~'Zm} p'Zm
{*=mAm*nYw6x(=
>qsm{w$
xsZp'*t9oNym{Yxsy*m>qsm{w$
xsZp'qsw6x(mtAw]x`w$/nQtOx(w6x(mN
{w$Yim>
{p$xsqsp'=Zmr p'qPxsy*mK7mqNp$,=/x(m{qOYmr*fw]x(m)tOx(w6x(mt>¢p'qPx(y*p$tsmvRw6xsyoXw8nt2
{p$*ZrJim?qOm{~'fw6xsm{r;
û
ACS Paragon Plus Environment
Page 13 of 30
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
The Journal of Physical Chemistry
¸
$¹ %(e' º c¦. k -gk g =[64#$k-/ ¶ *q[x(y*mp'qsmx(=
8w$*mxsy*pr
Zm{w$qsVnKv*qOp ¥$m{t`x(yRw]x`~'m{*mq(w$==nd
y*m{Z
{w$*qsm{w$
xsZp't3Z~$yx9v*qsp
{mm{rYw$Zp'~ x(ym?tOy*p'qx(m{txGvRw6x(y/oXw8n'zm¥$m{VExsy*mnHw$qsm)*p6xGxsy*m0w$tx(m{tx8 º poAm¥'mq{zp'*mZ~'y/xNw6tsHwQ¬*m{tx(=p'·V x(ym{tsm?*Vx(q(w]0w$tOx>vqsp
{m{tOtsmt2
8w6´imp'*tOm{qO¥$m{r·ZJqsm{w$.
y*m{Z
{w$.w$r´Zp'=p'~'Z
{w$itOntOxsm{t{ ² =xsy*p'*~$y
{qsqsm/x`tsZ~'Zm} p'Zm
{*=m[m v7mqs=Ymx(w$mxsy*pr*t9w$qOmP¬*=xsmPw$r ¥$w6*
{mr;z'x(y*mZqx(m{vip'q(w$ w$*rQtOvRw6xsfw$ qsmtsp'=x(=p'*tGw$qOmc*p6x2=|R*Vx(m{VnHvim{qO¢m
x{G¤\xTZtN=Yvip'qOx(w$/x>x(pYm{tOxsZYw6x(m)xsy*mdv*qOp'Rw$ZZVx(=m{t>w$r·x(=Ym ts
{w$Zmt>oNy*m{´x(y*mtsm?*=xsq(w60w$tx>v*y*m*p'm{RwZ~'y/xPx(w$$mv*Zw$
{m*tOZ*~qsm{w$Z=tOxsZ
p'*r*Vx(Zp$*t{ ªEpWv7mqO¢p'qO
û
ts*
yÄ
{w$Z
*fw6xsZp't{z*oAmdoNZ=.m{v*Zpn¿À Á>w$*rÄw$tOts*mcxsyRw6x
xû¾û
ts
{w$Zm>¢p'q[=x(qsw60w$tx`qsm8w6ZZ{w6x(=p'*tEp$gxsy*mN
y*m{Z
{w$Rv*qsp
{mtst[¤ Ww$rr*=xsZp';z6¢qsp'âÀ
(»¼P½
x(y*w6xQx(y*mJv*qOp'Rw$ZZVx n¼p$2p$*tsmqO¥Z*~atO*
yÃ*Vx(qsw60w$tOxKqsm8w6
x(=p'*tz
,À Á
Î
õ
õ
À¢í
Á,Vx`
8w$7m>¢p'*r
OzA
{w$Í7mJmtOx(=Ww]x(m{rÍw]xtsYw$Z
»¼P½ E w ¿¾ r J C =< C û º© x x x°
x(=YmtNw$t
~$=¥'mtTtTx(ymcx(=Ym
Á
û
À Õ Á ë
®
TpoäZmxX*tX
{p'*tOZr*mqPwd
ym{Z
8w6iqOm8w$
x(=p'Wx(y*w6xPv*qOp
m{mr*tPZYp'*mGx(q(w6*tsVx(Zp$YoN=xsy*p'xAZ/xsm{qsm} r*Zw6x(mKtxw6xsm{tÀ¢í¹é
§
t
W
û
Á2w6*rµx(y*mw8¥$m{q(w6~'mQx(Zmc¢p$qTx(yZt)v*qOp
m{tst)=tp$3p'qOr*m{q)p$3p'mKtsm
{p'*rgzιé
¹Ì¿m´w$r*r*mrÂm*nmJYp'=m{
*ZmtKx(p¼w$
{
m{=m{q(w]x(mLx(yZtv*qsp
{mtstJzAw$*rÔ=xQ=tw$tstO*YmrÔxsyRw6xx(ym
8w]xw$Vn m{rµqOm8w$
x(=p'µZtNxw6=*~Lv*Zw$
{m¥fwLw*moávRw]x(y/oPw8n·oN=x(yp'*md=/x(m{qOYmr*fw]x(m?tOxw]x(mHÀ¢åé ª>y*m
{w6xw6=nx(=
Tqsw6x(mtPw$qOmTx nv*Z
{w$ZVnp$;xsy*mp'qOr*m{qAp$òHé
û WÀWdW
x°
û
û W ± t § z ±s
û Á
U m6=zx(ymv*qsp
{mtstP=tPw$
{mZm{qsw6x(mr
xsZm{t{Aª>y*m{·¢qsp'ôÀ ÁXx(y*m?*Vx(q(w]0w$tOxGqsm{w$Z=8w6xsZp't>w$qsmxw6=*~v*fw$
m?¢p$qNxsZm{t>0w$tx(m{qNx(y*w$
û
Î;tzXoNy*Z=mHx(y*m´v*qsp$Rw$*=Z=x n«p$tO*
yÒm¥$m{/x(tY¢qsp'
û
"»k¼½ û W § °
À Õ ÁKZt
© M¤\2xsy*m*d7mq
p$`=xsm{qOYmr*fw6xsmtOxw]x(m{t2Zxsy*mdm*nYw6x(=
dvRw6xsy/oPw8nµ=t2Zw$qs~'mq{zRoNy*=
yÄ
{p'qOqsm{tOv7p$*r*t2xspHwWp'qsm?qsm} w$=ZtOxsZ
Yts=xsRw6xsZp';z,t(w8n¸å
é
Å z`xsy*m{¸xsy*mJ*=xsq(w60w$txKqOm8w$
x(Zp$*tQ
8w$ÍimHp'*tOm{qO¥$m{rÔ¢p'q
4»k¼½ û W § °
oN=xsy¸wµv*qOp'Rw$*=ZVx nÄp$
]x û WÀW
Îgt
£µ¤\xQ=td
{=m8w$q?x(yRw]x8z`w$Vx(y*p'~'y¿xsy*m{tOmLx(Zm{tdw$*r¸v*qOp'Rw$ZZVx(=m{t
w$qOmctOWw$= zxsy*mdvqsm{
ZtOZp'·p$9
*qsqOm{/x)m vim{qOZm{/xw$.xsm{
y**=¬*m{t=tNy*Z~'y·m{*p$*~'ytOpWx(y*w6xTxsy*mn´
{w$
ûÅ
ACS Paragon Plus Environment
The Journal of Physical Chemistry
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Page 14 of 30
imdp'*tOm{q¥'m{rg ¶ *md
8w$µtOm{mw$=tspx(yRw6xTx(y*mdtsvim{
{V|R
Kqsw$*~'mcp$`vRw$qsw$Ymx(mqstT¢p$q2p'*tOm{q¥ =*~L*Vx(qsw60w$tOx v*qOp
m{tstOm{tAr*m{vim{*rtAp'qsmfw6xs=¥$mP¥$w6Z*mt[p$g
ym{Z
8w6*x(q(w6*tsVx(Zp$Qq(w6xsm{t`ZQx(ymGtOy*p'qx(m{txXv*w6x(y/oXwnw6*r Zµxsy*mQ
8w]xw$Vn m{ravRw6xsy/oPw8naw$toAm{=[w$t)p'µxsy*mQr*V³gmqsm{
{mZxsy*mQ*Kim{q)p$AZ/xsm{qsm{rfw6xsmdtOx(w6x(mt Z´m8w6
yvRw6xsy; º p oAm¥$m{qz7x(ym{tsmc
8w$=
{*Zw6x(=p'*tPtO*v*vip'qOxTp'*qTw$qO~'*m{/x(t>x(y*w6x2p'txTvqsp'Rw6*=nLxsy*m{tOm *Vx(q(w]0w$tOx)vy*m{*p$YmRwH
8w$¼7mQm v7mqsZm{/x(w$ZVnw6
{
{mtstOm{r¸w$raxsm{tx(m{raoN=xsya
{*qOqsm{/x?m vim{qOZm{/xw$ mx(yp r*t
*1 -/.j&º (- g-/.ij ¹( 1 5 e Á ¤\xXoN=Zi7mT*tsm¢*.w$=tsp?x(pK=ZZtOx(qsw6x(m>xsy*ZtAv*y*m{p'Ym*p'H/nWw$Rw$Vn Z*~Kwdts=Yv*=m{q`p r*mixsyRw6xXtsy*poNt x(ymWt(w6Ym¬Rw$==xw]x(=¥$m7myRw8¥ =p'q?*xc
8w$¹im
{p'v*Zmx(m=nÄtOp'=¥$m{r¸w$*w$=nx(=
8w$==n$Ì¿mY
p'*tOZr*mqcx(ym *mx oXp'qOW=Là,=~*
û
û
oNy*m{qOm)w$=i*w$
/oPw$qOrJq(w6xsm{tPw6qsm2tOmxPxspK{mqspJÀ¢tsmmà,Z~* ÿ Á ² tAtsy*poNJZµÀ Á`x(ym
qsm¥'mqsts=*Z==x np$^x(ym2x(qsw$*tsVx(=p'*tAoN=Zi*p$x>
y*w$*~'mxsy*m)v*qsp$v7mqOx(=m{tPrZts
*tstOm{rJim{Zpo3ìx(w$qOxsZ*~c¢qsp' ²
x(ym?txw6xsm Þ z*x(ym?vqsp'Rw6*Z==x np$9qOm8w$
yZ*~Qx(ym?txw6xsmGßLw$Zp$*~Kx(y*mvRw]x(y
7:9
ò
q
*poÊtOZv*=nY~'V¥'m{´/n
û
À ÿ Á ê
ò ÍÎ
ts=*
{mKxsy*mQv*qOp
m{tst)y*w$t)*pHvip'tstOZ*=Z=x nHxspJqsmxs*qsµxspLx(y*mQtxw6xsm Þ w6§x(mqZm{w8¥ =*~LVx8ª>y*m{qOm¢p'qOm$z.x(ym
7%; ûÂ> 7:9
v*qOp'Rw$*=ZVx nxspqsm8w6
y´xsy*m)tOx(w6x(mGßw$Zp'~QvRw6x(y´ãÒZt>rm{ts
qs=7mr·/n
4rz9
v*qOp'Rw$*=ZVx nr*m{*tO=xsZm{t
Ãr;
EÀ ÁPw$*r
x
E`ª>y*m
p'*r*Vx(Zp$Rw$
`À ÁPw$tXr*m|Rm{r·w$7p¥$m)
8w$Jimm8w$tOZVnWp' xw$=*m{rL/nWtsp'V¥ =*~Kx(ym
x
^w$v*Zw$
{mx(qsw$*tO¢p$qs´z`w$tKtsyp oNÍm{w$qs=Zm{q ¯s
{p$qsqsmtsvip'*r*=*~ÄRw$
/oXw$qsrÃw$tx(mqQm{¬Rw6xsZp'*tcx(y*qOp'*~'y
Ãr9
ª>y*mWÀ0*p$qsYw$Z={m{rRÁ3v*qOp'Rw$*=ZVx nWr*m*tsVx n
,À ÁAoN=Zgx(w$$m)xsy*mm v*Z=
{VxP¢p'qs
x zr 9 ¢7 9 § DC oÄ Å @> û ÇÆ x < >Zû 9À ÁYé
µé
ò ó
ó
ç
§ § ®È §#É xÈ > C$ʳ© § ²É Ë
Á ç ó Î ç À0å
À
À
Á ó
ç
è*Á
Î ó
ûÕ
ACS Paragon Plus Environment
ê
À
û\ Á
Page 15 of 30
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
The Journal of Physical Chemistry
¢p'qv*qOp
m{tstOm{tK
p'*r*Vx(=p'*m{rÄxspqsm{w$
y¿xsy*mtOxw]x(mcßµw$Zp$*~´xsy*mvRw6x(y
Ìrn;
r*m*tsVx n
² Eì =Y=fw$qO=n$z7x(ymYv*qOp'Rw$ZZVx n
`À Á>w$=p'*~Kxsy*mvRw6x(y´ãË
8w$´im?p$xw$=*m{r´w$t
x
r; ¢7b; § C Ä Å Z> û ÇÆ x < >@û AÀ ÁYé
Î
õ
õ
ç
§ § È§Ê xÈ > C$Ê©³ § ²É Ë
õ ç Á ç ò ç À¢í è*Á
À
À
Á
õ
À ë
õ
ò
û|Á
TtOZ*~·x(y*mtsmLv*qOp'Rw$ZZVx nÄr*m*tsVx n«r*=tOxsqsZx(=p'*t{zx(y*mW
{p'*r=x(=p'Rw$[m8w6«|RqstxO}\vRw$tstsw$~'mWxsZmWw6*r p$xsy*m{qNrnRw$Z
)vqsp'vim{qx(Zmt>p$x(y*mtOntx(m{â
{w$w6ZtspQim
8w$=
{*Zw6x(mr´w$
{
p'qsr*=*~'Vn'
Í
àqOp'p op';z.oXmw$tOts*mQx(yRw]x?xsy*mq(w6xsmò«Zt)tOÐ
{Zm/x(=nµfw$qO~'m{qxsyRw$Äx(y*mq(w]x(mQÎÍtspJx(yRw]x
ÃG U ,G r %7 9pr9 y*m
*=*m´w$*rÔqsm{rÔ
{qO¥'mtW~'V¥'mLxsy*m·vqsp'Rw6*Z==x n¿r*m{*tO=xsZm{tQ¢qOp'ÜvRw]x(y vRw$qsw$mx(mqc¥6w$=*m{tct(w$mLw$tc*tsmr¸Z¸àEZ~* Õ
AÀ ÁT¢p'qx(ymv*w6x(y¿ã
²
w6*rÃãTz[qsm{tOv7m
xs=¥'m=n$zAoN=xsy
m
{m{v xQ¢p'qcxsy*mWRw6
oXw$qOrÔqsw6x(mtdxw6$m{¹xspµimWm{¬Rw6
x(pJm{qspY¤\x
Zm8w6qs=ntsy*poNtx(yRw]x?xsy*mtsy*p$qOx(mqvRw6x(y¿ãÈyRw$t?wHy*Z~'ym{q)v*qOp'Rw$*=ZVx n·xsyRw$ax(y*mZp$*~'m{q vRw6xsy
²
w6xdtsYw$Z`x(=Ymtdm¥$m{¸x(yp'*~'y¹xsy*mL¢p'qsm{q?p'*mH~$=¥'mtKts=poXmqKZ*mx(Z
tGÓO*txw$tKv*qOm{r*=
xsm{r
7:9
¢qsp$p'q>v*qsm¥ =p'*t>r*=ts
*tstOZp'*t ² x>x(y*m)tsw$YmxsZm$zx(y*mxsp$xw$7v*qsp$Rw$*=Z=x n tOx(w6x(m´¢qsp'xsy*m´Zp'*~$m{qvRw6x(y
²
xspQqsm8w6
y´xsy*m|RRw$
=tYyZ~'y*mqQx(yRw$Âx(yRw6x¢qsp$x(y*m´vRw6xsyÒãim{
{w$*tsm·p$xsy*m·0w$tx(mq
Z*mx(=
{toNy*m¹òÍöáÎ,K¤\xZt)
p'*ts=tOxsm{/xoN=x(yÄxsy*mp'*tsmqO¥6w6xsZp'Äx(y*w6xx(ym=p'*~'mqÀ¢0w6tOx(mqÁvRw6xsy
²
oNZ=7y*w¥$mwKy*Z~$y*m{qAv*qsp'*w$*Z==x nw6xXZ/x(mqsm{r*Zw6x(mGx(=YmtAoNy*mqsm)p'tOx>p6.x(y*mqOm8w$=Z{w6x(=p'*t3p$m¥'m/x(t w$qOmGp$xw$=*m{rg9¤ /x(m{qOm{tx(Z~'=n$zoAmT¢p$**rx(yRw6xA**rm{q`x(y*mtsmG
{p'*r=x(=p'*t[x(ymTtOy*p'qOxsm{txXvRw]x(yYoN=Z*y*w¥$m wdy*=~'y*mqXv*qOp'Rw$*=ZVx nw$~/w$=Ww]xPm¥$m{Jfw6qs~'mq3xsZm{t2À0tsmm)à,=~*
\
Á9ª>ymx(y*=qsrWqOm{~'=YmGZtA**mvim{
x(mr;z
û ÿ
ACS Paragon Plus Environment
The Journal of Physical Chemistry
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Page 16 of 30
e û
= û § È§Ê x
*x9=x[=t,m8w6tOnKxspm v*Zw$ZQVp'*mP=p p't[w]x,x(ym>m v*Z=
{Vx9m v*qOm{tOtsZp$*t `¬À Å Áw$*r [¬iRÀ Õ ÁE¤ r*m{mr;z x(ym?rp'Y=Rw$/xXxsm{qO ãËw$*r
x
§ È §#É
ó
xw6ZEw6x)fw6qs~'m
x
w6xNfw6qs~'m
x
ZHip$xsy´m v*qsmtsts=p'=tPv*qOp'v7p$qOx(=p'Rw$ix(p
eÎ
õ
¢p'qPx(ym)vRw6x(y/oXw8n
² zoNVx(y·òöMÎ9 X=m8w$qO=n'zx(y*mvRw]x(y/oPw8n´ãMoNZ=gyRw8¥$mxsy*mfw$qO~'m{q
¢p'qXxsy*mvRw6x(y/oXw8n
?ª>y*tzw6§x(mq)wLtsÐ
Zm{/xs=nµZw$qs~$mcx(=Ym6z7xsy*mKv*qOp'Rw$*=ZVx n´xspLqsm{w$
yax(y*md|*Rw$9txw6xsm
x(yqsp'*~$y¿x(ymYvRw]x(y
²
oNZ=97mYtsYw$Z=m{q)im{
{w$*tsmYYp$tOxcp$Xxsy*mWv*qOp
m{tOtsm{tcx(y*qOp'*~'y¼x(y*=tcvRw]x(y«y*w¥$m
w$=qsm8w6rnQp
{
{qsqsmr; ² x3¥'m{qnfw$qO~'m>x(Zm{tz/x(y*mGWw6Z
{p'/xsqsZx(=p'Qx(pdqOm8w$
yx(y*mN|RRw6itxw6xsmT=t3w$~/w$= p'tOxs=na¢qsp'Ùxsy*mLvRw6xsy¹oN=xsy¹ts=p oAm{qKxsq(w$ts=xsZp'¿q(w6xsm{tĪ>y*mH
{p'/xsqsZx(=p'*tc¢qOp'Ùx oXpavRw]x(y/oPw8nt Ywna
y*w$*~'mWw6x?Z/x(mqsm{r*Zw6x(mw$*r¿fw$qO~'mQx(=Ymtcw6
{
{p$qsr*=*~´xsp·xsy*m¥6w$qOfw6xsZp'ap$XZ*mx(Z
tc=¿m{w$
y vRw6xsy/oPw8n'ziy*poAm¥'mq{z;VxGw$v*v*=ZmtG*=¥$m{qstsw$ZVnLx(y*w6xTxsy*m?tsy*p'qx(mtOxTvRw6x(y/oXw8nµw$VoPw8ntG~'=¥$m{tNx(y*m?y*Z~$y*m{tx v*qOp'Rw$*=ZVx nYxspqOm8w$
yJx(ym|*Rw$.tOx(w6x(m?w6xNm{w$qsVnWxsZm{t>qsm~/w$qOr*ZmtstNp$x(y*mZ*mx(=
{tNp$x(y*mtOntx(m{´
·Ý
Ý
ÐÏ
ÚÜ
ÚÜ
ÛÂ
H[
Ì¿my*w¥$mY=/¥'m{tx(=~/w6x(mr¿tx(p
yRw$tx(Z
rnRw6Y=
{t)Za
p'YvZmµ
y*m{Z
{w$[w$r¿*=p'Zp$~'Z
{w$^*mx oAp'qstcn w$Rw6=n{=*~Jv*qsp'*w$*Z==xsZm{tw$*rax(Zm{t)¢p'qtOZ*~'=m}\Yp'=m{
*Zmcqsm8w6
x(=p'*t
²
{p'v*=matn tx(m
*tORw$==n
{p$x(w$Zt?Yw$/nÄ
p'YvimxsZ*~Hv*w6x(y/oXwntdw$tts**tx(qsw6x(mZt)
p'/¥'m{qx(mr«x(p´v*qspr**
x8QÌ¿my*w¥$mW=*r*m{mr
{p$*ts=r*m{qOm{rÒx oXpÍqOm¥'mqstOZ*=mÍÀ0p'qWZqsqOm¥$m{qstOZ*=mÁYv*w6x(y/oXwntJp$*m{¬Rw$)=m{*~$xsy*tWoNy*mqsmµxsq(w$*tO=xsZp'*t imx oAm{m{Íx(ymHZ*Vx(fw6`w$*r¸|RRw$AtOx(w6x(mtQp
{*qKxsy*qsp'~'y¹x(y*mH=p'*~'mqdvRw]x(y¹0w$tx(m{qQp$Íw¥$m{qsw$~'mLx(y*w$ ¥fw·xsy*mLtOy*p'qOxsm{qQqOp'x(m6
² tQmvim{
x(mr;z3xsy*mWxsp$xw$3v*qOp'Rw$*=ZVx nÄx(pÄqsm{w$
y¹x(ymL|RRw$AtOxw]x(mWxsy*qsp'~'y
x(ymWZp$*~'m{qvRw]x(y«oN=Z[Z
{qsm{w$tsmWw$*r¿7m
{p'mWy*=~'y*mq?xsyRw$¿xsy*mWtOy*p'qx(m{qcvRw6xsy¹=A0w$tOxsm{qcxsq(w$ts=xsZp' q(w]x(m{tXw$qsm2w$tstOp
fw6xsm{rx(pcxsy*ZtAvRw6xsy;[ãXmtsZrm{t{z=x`xw$6m{tP=m{tOtAx(=Ym>¢p'q`x(ymqsm{w$Z=8w6xsZp'p$;xsy*m2vqsp
{m{tOt x(yqsp'*~$yxsy*mNZp'~'m{q9v*w6x(yoN=xsyK0w$tOxsm{q[x(qsw$*tsVx(=p'*t9=w¥$m{qsw$~'m$`àRqOp'Ñxsy*m{tOmGp$*tsmqO¥6w6x(=p'*tzVx[tsmm{t x(y*w6x,xsy*mPvRw6xsy/oPw8ndoNVx(ydxsy*mA0w6tOx(mtOx`Zmx(=
{toXp'ZrQw$VoPw8nt9r*p$Y=Rw6x(m`x(ymXx(qsw$*tO¢p$qsYw6x(=p'cvqsp
{m{tOt p$v*qOp r*
xE¢qsp'Èts*tOxsq(w6xsm$z'=qsqsmtsvim{
x(=¥$mPp$Rp6x(y*mq9v*qsp$v7mqOx(=m{tp$Rx(ymXtOntx(m{´ º p oAm¥$m{qzVx,=tE¢p'*r x(y*w6x8zR=´
p'/x(qsw$tOxNx(pmvim{
xw6xsZp't{zRx(y*mYw ÓOp'qP
p'/x(qOZ*xsp'qst>¢p'qPxsy*m?qsm8w6ZZ{w6x(=p'Lp$|RRw6.v*qspr**
x
û\
ACS Paragon Plus Environment
Page 17 of 30
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
The Journal of Physical Chemistry
¢p'qOWw6xsZp'¿w$qOmW*p$xKw$=oXw8ntdx(y*mWvRw6x(y/oXw8n tKoNVx(y«0w6tOxK=*mxsZ
{tµ¤ *r*mm{r;z9oAmHyRw8¥'mWtsy*poNÍZ¼x(y*=t oAp'qsWxsyRw6xNx(ym{qsm=tNw$=oXw8n tGwKx(=Ym2ts
8w6Zmw6xNm{w$qsVnWx(=YmtPoNy*m{Jx(ym?tOy*p'qx(m{tx2v*w6x(y/oXwnHoN=Z77m)x(ym Yw$Z?qsm{w$Z=8w6xsZp'p$*xsy*mX
ym{Z
8w6vqsp
{m{tOt{9¤ Kw$r*r*Vx(Zp$;z6tsZ~2qsm{w$Z=tOxsZ
[vRw$qsw$mx(mqstoXmPmtOxsZYw6x(mr x(=YmtO
8w$=m{tw6*rµv*qOp'Rw$*=ZVx(Zmt>p$[p'tsm{q¥Z*~Wxsy*m{tOmKv*y*m*p'm{Rw ¶ *qT
8w$=
{*Zw6x(=p'*tNZ*rZ
8w]x(m)x(yRw]x *Vx(q(w]0w$tOx>vy*m{*p$YmRwZ~$yxP7mp'*tOm{q¥'m{r*ts=*~Ypr*m{qOJm v7mqs=Ymx(w$;x(m
y**=¬m{t{ ² tXxsy*m2¥Z~$p'qsp'tA~'qOpo>x(yHp$.tOZ*~$ZmGYp'=m{
*ZmNx(m
y**Z¬*mt{zRVxX=tA*poävip'tstOZ*=mTx(pdp'*tsmqO¥$m)*=xsq(w]} 0w$tx)qsm{w$
xsZp'*t2ZÄYw$/n
y*mY=
8w$Uzgv*y/nts=
8w$Uz.w$*ra*=p'Zp$~'Z
{w$.tOntOxsm{t?w$*rÄ*mokv*ym{*p'm{*w´w6*r m{
yRw$Ztstw$qOmYw6xsZ
ZvRw6xsm{rµxsp´imr*ZtO
{p¥'mqsmr;Yª>yqsp'*~$y¼xsy*m{p'qOmxsZ
8w6[w$Rw$VntsZt2p$Axsy*m*mx oAp'qO tOntx(m{t{z7oXmcp'*tsmqO¥$mdx(yRw]x2x(ymdv*qOp'Rw$*=ZVx nWx(pYqsm{w$
yµx(y*m?|RRw$^txw6xsmdZtTwYrm{
{qOm8w$tOZ*~Y¢**
xsZp'·p$ x(=YmG¢p'qAxsy*m)tsyp'qOxsm{tOxNv*w6x(y/oXwnLw6x>m{w$qsVnxsZm{t ² *rLxsy*mYw ÓOp'qsVx np$^x(y*m=x(qsw60w$txPqsm{w$Z=8w6xsZp't{z
b0Çye{Çgqsm{w$Z=8w6xsZp'tXx(yRw]xTqOm8w$
y´x(y*m)|R*w$^tOxw]x(mGßWZ·wQx(Zm=m{tstNx(y*w$w
{mqOx(w$ZJ¥6w$Z*m
x
zZt>tO*qsv*qOZt&}
Z~'=nY¢p'**rJx(p
{p'm)¢qsp'x(y*m?tsy*p$qOx(mtOxTvRw6xsyoXw8n'Pª>yZtGv*qsp'vim{qx nJp$E*=xsq(w60w$txGqsm8w6
x(=p'*tNZt>p$*=n r*mx(m{qOY=*m{r¸/n¹xsy*mLtx(qs
x(qsmJp$Nx(y*mHmx oAp'qs¹x*p$xKxsy*mHZ*mx(=
{tKp$Nxsy*mHtOntOxsm{´
¶ *mH
{w$
v*qOp ¥=r*mxsy*mY¢p$ZZpoN=*~Hts=Yv*=mm v*fw6Rw6x(=p'¼p$Px(yZtv*y*m*p'm{*p'g´ª>ymWm8w6qs=nÄxsZm7myRw8¥ =p'qp$ x(ymT|RqOtOxO}\vRw$tOt(w$~'m2r*m{*tO=x nWw$Zp$*~dw?vRw6xsyWx(yRw]xP
{p$**m{
x(tXxsy*m2=*=xsfw$tOxw]x(m Þ w$*rWxsy*m2|R*w$7txw6xsmPßK=t r*mts
{qOZim{rH/nHwcv7poAm{q>fw8oËr*=tOxsqsZx(=p'
xjÑ
4Ò
oNVx(yWxsy*mm vip'*mx ¼~'=¥$m{H/nx(y*m*d7mqPp$^tOx(w6x(mt
w$=p'*~cxsy*mvRw]x(y/oPw8n$§¯sO¨ ¯ ¯>ª>y*mqsm¢p'qsm6z*=xAZtAm8w$tnWx(pdp'*tsmqO¥$mx(yRw6xPwdtsyp'qOxsm{qPvRw]x(yLoN=xsyLZmtstP*d7mq p$gtOxw]x(m{tA~'=¥$m{t3fw$qO~'m{q9¥6w$=*m{t`¢p'q[x(ymTv*qOp'Rw$ZZVx nKr*m*tsVx nQx(pcqsm8w6
yYx(ymG|R*w$tOxw]x(mTw6x3m8w$qO=nQx(=Ymt{ ¶ *qd
p'*
{=*ts=p'*tcr*pµ*p$xcr*mv7m*r¸p'«xsy*mW*Kim{qcp$Nqsp$x(mtd*p'q?x(y*mx(p'vip'=p'~$nÄp$Nmx oAp'qst
û
û
w$*r¼ts=Y=fw$q2m v*qsmtstOZp'*tdw$tYÀ Áw6*rÒÀ Å Á2
8w6«imYp' xw$=*m{rats=Yv=nµ/n¼m{v*=p n=*~Hx(y*mm vRw6 } ts=p'Hx(m
y**Z¬*mr*m¥'mZp'vim{rJ¢p'qPx(ym)~'m{*mq(w$.mx oAp'qsHtn tx(mYt§¯ ¯2ª>y*mqsm¢p$qsm$zVx>ts*~$~'m{tx(t>x(yRw]x>x(y*=t
{p$*/x(m{q&} =xs*=xs=¥$mdp'*tOm{q¥$w]x(Zp$ÄZt)wW*=¥$m{qstsw$9v*ym{*p'm{p'¼w$*rÄZ~'y/xTZ*r*=
8w6xsmKwW¢*rRw$m{/xw$ m{
yRw$Ztsá~'p¥'mqs*=*~Ww6nc
y*mY=
8w$w$*rQ*=p'Zp'~$Z
8w6/tOntOxsm{t{`»Nm{
{m/x`tOx(r*Zmt[tsy*poÔx(yRw6x9Ww$/n *Vx(q(w]0w$tOx2qsm8w6
x(=p'*t)
{w$**p$ximQ**rm{qstx(pp ratOZv*=nJ¢qsp$
xsy*mQZ*mx(Z
dv*qsp'vim{qx(=m{t)p$`x(ymQtOntOxsm{´
û|
ACS Paragon Plus Environment
The Journal of Physical Chemistry
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Page 18 of 30
¶ *q2|Rr*Z*~$tY=~'y/xw6tsts=tOx)=µ**rm{qstxw$r*Z*~Lxsy*m{tOmQ
{p'v*=mv*y*m{p'YmRw ¶ *qtx(*r nµ
8w6aw$ZtOp v*qOp ¥=r*mw´tOZv*ZmdoXw8nax(pJr*Ztx(=*~'*=tsyÄx(y*m
p'/x(qs=*xsZp'*t)¢qOp'x(ym¥6w$qOZp't)qsm8w6
x(=p'¼vRw6x(y/oXw8n t ¤\xKtOy*p'*=r«=m8w$r¼x(pimxOx(mqd**rm{qstxw$r*Z*~·p$>m{
yRw6*ZtOYtcZ¼
{p'v*Zm¼tOxsp
yRw6tOx(=
Wtn tx(mYt·Ì¿m im{Z=m¥$mx(yRw]xH=xYoNZZGimÄv7p'tOts=*Zm´x(p¹¥'mqsV§nMp'*qWv*qsmr*Z
x(Zp$*tLm vim{qOZm{/xw$==nÔ/nâp'=ZpoNZ~¿x(ym ts=*~'=m} p'=m{
{Zmx(qs*p¥'mq)Z
big hNbimyk&z?m v7mqsZm{/xst2oNy*m{qOmKx oXpHr=³7m{qsm/xqsm{w$
xsZp'qsp'xsm{t
{w$Äim
r*=tOx(=*~'*=tsy*mr;Hª>y*mWx oApµ
p'YvimxsZ*~´vRw6xsy/oPw8ntQtsy*p$*Zr¿
{p'/xw6Z¹w´Zp'~·qOp'x(mx(yRw]xd=t?¥$m{qOn¼0w$tx oN=xsyÄtsYw$Z=m{qTYm{w$µx(*qO*p¥'mqxsZm{tz;w$*r¼wLtOy*p'qOxsm{q)qOp'x(mKxsyRw6x)=tts=pok=Äw8¥'m{qsw$~'m6Kª>y*Zt2
{p'*=r imqsm{w$Z={mrÂ/nÔ
{p'tsZrm{qs=*~¹w¼ts=*~'Zm} p'Zm
{*=mHqsm{w$
xsZp'ÔoNy*m{qOm·x(ym·x(qsw$*tO=x(=p'Ôq(w6xsm{tW
p'*=rÃim Z
{qsm{w$tsmr/nLxsy*mc
{w6xw6=nts=t>p$[wQtsvim{
=|R
?m{nYm6Aª>ym{xsy*mtsy*p'qx(mqGv*w6x(yJ¢p'q>x(y*mqOm8w$=Z8w]x(Zp$Lp$ ts=*~'=m} p'=m{
{Zm)x(*qO*p¥'mqoNVx(y*p$x)m{nYmt)oXp'ZrÄyRw8¥'mwLtOZpoXmq)Z*mx(Z
t
{p$YvRw6qsm{rÄoNVx(yµx(ym Zp$*~'m{q>p$*moN=xsy·m*nYw6x(=
)qsm8w6
x(=p'*t
Á4 5 j h)(k-g: Ó Ô
Ð
² ã2 lQw$*r K [w$
*poNZmr*~'m[x(ym[ts*v*vip'qx.¢qsp'
Wû Ö ºk k , [ Ø× û
ÕÎ û
û W û Æc W Õ'Õ d]}
2w6xsZp'Rw66¤ *tx(Vx(xsm[p$ º m8w6=x(yYÀ »
ÁPw6*r´xsy*m)Ì«mZ
y·àRp'**rRw]x(Zp$¼À 3} ÿ'ÿ /Á
À ÁHãXyRw$=fwz c ì7 R¤\n'm{~/w$q{z» [m{qs~$m{/xNv*qsp$v7mqOx(=m{t>p$*mx oXp$qstTp6EZp'=p'~'Z
{w$ts=~'Rw$=Z*~cvRw6x(y}
Q ^cbdegc&eÙ[ÚzÚzÚ;zW¥cÛÝÜ'z Å û } Å |
oPw8nt{
Ô Ø×Þ àß Ø× $á Q}Sexbdcvj a evcmobdz
gâZemã
z k&NlLä(å §ákÖvtS ^Se&z
k&emybdcvjzå tKtXk$z¤vc& zÎ ?ÎÐ} û d \ æ Ø× $á ç× Ø×zÎ $æ èæ zÎ âvjm .a eh á§Begem né êzêÙ W¥ d\ |
À ÁLªEmYZgz ¶ c gmZ~/w6qs*=iz ² K ãXp$*
y*m¥iz K5ÆQ z P»
ÀÅ Á
[qsmtstz7ãAp
{w»Gw6xsp';z
º w$tx n'z i·
·=Z=m{;z K *¤ tsw'w$
t{zàX Xp'=ZZt{z Xp$Yv* xw6xsZp'Rw6gtOxs*r*=m{t>p$E~'m{m)qsm{~$*fw]} x(p'qnH*mx oAp'qOtuA=JYmqspYp'=m{
*fw$qA*Zp$Zp'~$n$
\Ç
]Ç
û
ACS Paragon Plus Environment
Ç
Rz /z
]}
Page 19 of 30
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
The Journal of Physical Chemistry
Ô Ø×
,Þ ë , Õì zâëvjm .a eh á§Begem é êzêzí . û W û ûjû ëÎ ç×[ nëâ vjm emiSz¤
l?ézêzêî . û W Ø× Ø× «âvjmB emiSz¤
l \ ézêzêî . W | û\ Ø× ç× Ø× æ ç× ç×Î Ô ß | zëâ vjmyk&eÙ#ÚÚzÚ S£K W á ç× Î } Ø× nÞ Ø× æ Ø×Î Ãß á =} \k$zNc âvjmo 1åCcvK ^cb CfQ [åfé êÙcê W¢ |À| \ |À| W "ï Ø× næ Ô Ø× Ø× ç× #ï Ô Ø× z} ß · V ^cbdegc&e û ézêzêð Ü K d\ W û d\ W Ø× ë åCgSg a eh ûW ênNl á}Sex ézêzêpñ QÀÛ \ | \ :Î ë Ø×D} Ø×%} æ Ôá ûjû Cå gSgS .a eh Q bdz&tSnNl né êÙcê 1Ücò û û \ 6bigj,eP z
é êzêkÙ W¥ À\ û Ó Ø×:Î ëá ç× :æ û \ bdz
mue&c&gz
ó nézêzêÚ S£ \ c| û À Õ ÁHãPw$q(w6Rw$tsUz ² ` ~/w$*=8w6xsZp';
¶ Vxs¥6w$ z , ? Tmx oXp'qOa*Zp'=p'~$niu*r*m{qOtOxw6*r*Z~·x(ym
m{= t¢**
xsZp'*w$[p'q}
Ç
]Ç
\Ç
^z $z
}
Å
Tm{Ww$gz lQ 2 2w6~$n ² ìZ*~'=m}\Yp'=m{
*Zm3¢p'qs
mGtOv7m
xsqsp'tO
{p'v/niu[p'vxsZ
8w6*x oXmm{{mqstzYw$~'*mx(Z
Àÿ Á
x oXmm{{mqst)w6*r´w6x(p'Z
T¢p'qs
m?Z
qsp'tO
{p'v/n$
À ÁH»Gpn'z9»?
º wzEª) ²
º p'y*~*z`ì7
;z $z ÿ
} ÿ
;z $z Õ
v*qsp
{mtstsV¥'mcw$
xsZ }\Rw$tOm{r´Yp$xsp'q{
;z
]z ÿ
**;z ² » Xy*w$;z E RãXqn/w$/x8z , ì v*r*Z
y;z ²
} ÿ
Xy*m*mn$z»? >´n$p'ts= } È=t>w
Å
Xp'/x(qOZ* x(Zp$Hp$Exsy*m?´n$p'ts=
p'Ww6ZYxsp `qOp
m{tOts=¥$mcìx(mv*v*Z~w$*rJ¤ /x(q(w6Yp'=m{
*fw$q3ªm{*tOZp'·ì m*ts=*~* 0Ç
^z
8z
}
6Õ
ÿ
}
VÇ
ÿ } ÷Zp
8w6ZZ{w6x(=p';
z
ÿ
ÁHlp$Zp'm{=ts/n'z ² ã2 AàEZtsym{q{z[¿ >9·p'Zm
{*Zw$q?Yp$xsp'qstuQw´xsy*m{p$qsZtxKvim{qOtsvim{
xs=¥$m$
À
À
{Ç
Á
Ç
² =xs$m;z 2 >
p$Exsq(w$tsfw]x(Zp$;
À Á
7z
'z
ÿ }
Emx(qOp ¥iz ² Ç
]Ç
[*~'=ZtO z K^ì =*~'ZmdqsZip'tOp'YmdrnRw$Z
{tw6*r¼xsy*mYm
yRw$*=ts
]Ç
XqsmYmq{zÆQ m6
tsZ~'Zm} p'Zm
{*=m2Zm¥'m
iÇ
ÿ
{Ç
^z
$z Õ
} ÿ Å
Zm6zì7iì =*~'=mYp$Zm{
*Zmw$v*v*qOp/w$
yJx(pm{*n p'=p'~$n'
À 8Å ÁHãXfw$iz;l
/Ç
º wzRª) gÆ)p'Zr*Yw$;z Q N gì m{V¥ =;z E »gJn'p'tOZ
îoPw$=tGy*w$*r }\p ¥$m{q&} yRw$r;zRts=*~'Zm R*p'qOp'v*y*p'qOm)ZYw$~'=*~coNVx(y ]z
{Ç
2¤XªEw$Z
À /Á )Z=r*Z6z ² 7àp$qs$mn'z c ;·
{l)Z**mn'zgì7 ²
;z
ÿ
v*q(w6
x(=
8w$3~'*=r*mx(ptOZ*~$Zm}\Yp$Zm{
*Zmà,» [ª
À ÁJ·m{y/xw z ² R»Gp
zR» R»NZm&zR¿ ì v*r*Z
ygz ´p p'tOm{6m{q{zi¼
À /Á
} ÿ
VÇ
Rz /z $ ]} 6Å
º p$¢$m*t{z .à,=*p'qOm{ts
m{*
m}\Rw$tsmr«w6Rw$=ntOZtp$3m*nm{t?w6x)x(ym VÇ Ç
;z Rz Õ /ÿ } Õ
ACS Paragon Plus Environment
The Journal of Physical Chemistry
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
û
!âvjmok$e4é êzêÙ S£X¢ d\ | \
À Õ ÁJìx(qOp'~/w6xs$zì7 º , v*Zp$qsZ~Q
{p'v*ZmH*mx oXp$qst
næ Ø×1æ aeut é êÙ[ð .j¥#ò û À ô\ ,ï Ø× ëá Ø×D ®û \ á ézêzêõ S£zSÜ û\ j û æ èæ Ø× û| û
À ÿ ÁJÆp' x(tsZw$t{z gÇ
z
]z
]}
QênNl{Ç
$m*Z*tOp';zgÆ7w6qs$p¥fw6rnRw$Z
tTp$
{p$Yv*=mJqOm8w$
x(=p'*mx oXp$qst{
;z
$z
]}
Õ
ÁJì poPwz Q 9»NpoXm·z ² K
À
Page 20 of 30
ëÎ ç×kï
.m8w6$m$z,¿ 2
ç×
Aw$*tsy*Uz^ª)
Ø×
ç× âëvjmy k$e
º p'Ww z^¿ ,¤ tsy ÓOZYwz ² EãXm{qOqOn$z
·
»? ¿ ZqOm{
xp'*tsmqO¥6w6xsZp'Íp$TtOxsm{v*tZÍqsp6xw6xsZp'¸p$Gx(ym´*w$
xsm{qsZw$ w6~'m{=fw$qKp$xsp'q{ ;z
À
8z
}
$ Ø×#
c ç×[
Ô Ø×$æ
èæ Ø×[á âëvjmyk&eHé êêö £K£S¥
ÁHlmqstOtsm{Yw$6m{qstz ÌÈ ·*/x(m{w$;z [ w$w$;z [ Tpmxs{m z/ª) ` 'w$*tsp$;z ¿ p'~$x(mqsp'´z ¿ ² tstOm{K=nÍrnRw$Z
tp$2Z
qsp$xs***=m{tw6xp'Zm
{*Zw$qKqOm{tsp$ZxsZp'*t
|W |û ]}
û
;z
C 6muzNc&8v
lmybdc k$zNc&e&l&lNe&l big }Sexb,lmykwnËvjgXnNlbdc&l û À ?å §ábye%muzr÷ bik&lmydáv
l&l¤vNe k$zNc&e&l&lNe&l 4Î l}
À /ÁW¥$w6þlw$v7m;z c Æ ² tOx(mqsrRw6·z
û
z Tp$qOx(y
ÀW W û R} ç×
*qs=r*~'m$z
W
º p$Zfw6*r;z
À /ÁH»Gmr**m{qzìi
À
/z
z Pw$d*qs=r*~'m
G*=¥$m{qstO=x n
Î
[qsm{tOt{z Pw$}
ç×øß
ÁHlmZ=m{q{z $»Gpm{==n$z]ì7 3w$Z=m{qOfw$*Uz ² ²
¬Rw$ts} qsw$*r*p'Q}\oXw$=Gxsp>Ypr*m{'wNZp'=p'~'Z
{w$x(qsw$*tsvip'qx
^ emÞSz¤z
VÇá}z
xCtXm Ç1åátKtXVÇ.k$zdù&vÝùÇZzzé êÙ#ð.z.¢K$z û } ûÅ
v*qsp
{mtst{
û Á^UzÝÓKØ×*l)p'Zp$YmZts/n$z ²
À
ã2*´m{
yRw$ZtstPw6*rWx(p$v7p'=p'~$ndr*mxsm{qsZ*w6x(=p'Yp6;
{p$Yv*=m
y*mY=
8w$
ó ;}Sex SênNl
w$*r*Zp'=p'~'=
8w$*mx oXp'qOQtOntOxsm{t3¢qOp'Ñ|*qstOx} vRw6tst(w6~'mGxsy*m{p$qsmxsZ
{w$Rw$v*vqsp/w$
yg *Ç
ézêÙ#ð .¢ÀÜcò û û W \ ß Ø×b ÂÓ ç× ;z
À $ Á
$z
Õ'Õ
3w$Z=m{qsZw$*Uz ²
Ç
{Ç
Â
. z d l)p'=p'YmZtOn$z ² ã2 G/¥'m{=Z=*~«x(ymÄy*Zr*rm{ÒtOxsqs*
x(*qOmÄp$
{p$Yv*=m
ó á}Sex Qn_l é êkÙÝí .¢¤£ W \ û W û
tOx(p
yRw$tx(=
?Zp
y*m{Z
{w$g*mx oXp$qst{ Ç
Ç
{Ç
^z
W
ACS Paragon Plus Environment
]z
Õ
Page 21 of 30
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
The Journal of Physical Chemistry
Ó Ø×
Ø×Hß
^Uz K Yl)p'=p'm{ZtO/n'z ² ã2
À 6Å Á
}
3w$Z=m{qsZw$*Uz ² Ew6x(y/oXwnÊtOx(qO*
xs*qsm«r*mxsm{qsZ*w6x(=p'É=þ
p'}
zó }Sex ênNl zé êkÙÝí W¢¤£
v*ZmLtx(p
yRw$tOxsZ
)*mx oXp$qst>oN=x(yW*p' }\m v7p$*m{/x(Zw$gr oXmZgxsZm{t{ Ç
ûÕûW
á
À Õ Á
%Î Ø×%
m{*m$m$z 2
ç×,ß
Ç
{Ç
Î
^z
3w$=Zm{qOfw$ z ² Xp'v*=mÄrm{~'qsw$rRw6xsZp'Äv*qOp
m{tOtsm{tcZm{w$rµx(pJ*p'}
.ZvipoNts/n'zE»
4 úQz_ ²
m v7p$*m{/x(Zw$Xrm{
8w8n¿vRw6xOx(m{qO*tQw$rÍw$~'m}\r*m{vim{r*m{/xQr*m
8w8n¹qsw6x(mtKp$>m{tOtsm*~'m{q»
û ge8é êÙ#ð Û ç×dá ¢ôÛ |
]z
.z 'zm ÿ'ÿ Õ$Õ
Rß ø}
6}eié êzêé.z
À $ÿ ÁHàmqstOyx{z ² » )w$~'~'mxsx8z K [qsp6x(m{=c¢p'=r*Z~Nw$*rd¢p'ZrZ*~Gw6x,w6x(p$Y=
[qsm{tOp'Z x(Zp$; 'z ÿ
ô\
À
Å } ÿ
Ø×n}
ÁJì
y*pm{*=m{Zgzg» ÌÈ
1 Ø×
ç× ,Î àß ^cbdegc&e Ù#ÚzÚÙ W¥¤£ û û
Emxsm8w$;z ` ² .·w6x(y*=m{tzg» ² gì yRw6*z 2 Kiª>y*mc|RqOtOx2tOx(mvµZ´¥Zts=p';u
¢m{dxsp'tsm
{p'*r·ZtOp'Ymqs=8w6xsZp'Yp$,qOy*pr*p'v*tOZ;
Ø×
|
À
[ß Ø× Ìý ü
ÁH»Gm*~'m{qzª) Rw8n$z K *l
$
Rz
Rz Õ } Õ ÿ
y*;z ¶ G=xsq(w60w$txXm
{=x(w6x(=p'm{*mqs~$nx(qsw$*tO¢mqXrnRw6Y=
{tX=Wv*yp$x(p6}
nNl{Ç.aeutgÇé êzêkÙRz,Ü£zÜ'z û8Å | } $ÿ Õ
tOn/x(y*mx(Z
?v*=~'Ym/xO} vqsp$xsm{ZH
p'v*Zmmt{
þÎ
À /Á
ç×
ç×
Xy*~*z º ì7 g·
º w$=m$zilQ
á
b}
æ ç×n
.p'*=t{z ¿
Ã}
v7mqsZm{/xst mx(m{qOY=*m [qsp$xsm{=àRp'=r*Z*~ªq(w$ts=xsZp'
À
Ew6x(y·ª>Zm{t{
$z
eåCg gSmyk$z¤j6cmybdz
gTmuz 6m|zNc&8v
lmybdc z¤e¯big } Ìá û dÀ ç×z Ø×n zá pì W ß ,ÿk .ênNl kúQemom pé êzêî ¾Û ¥ W ûjû ç× ç× Âæ èÎ Ø×} (æ Ôá nNlbdcvj}Sexb,lmykn kwbigcbHtX,e&l¦vjgX û åátKtX¯bdcvjmybdz
g8lbig bdz
,zjbdcvj ^cbdegc&e&l } ( ? ¤æ WÀW `qOm{tOt{z7ìw$
ç×
3w$Z=m{qsZw$*Uz ²
Á
}
$z [=tsm¥=m{q ²
{w$r*mY=
Zm~'p*z Å qsr´m{r*Vx(Zp$;z
Z
8w6;tOxsm{v*t
ÀÅ
;z
Õ
À /ÁLª,w8nZp'qz º 5¼ Glw$qs=Z;z3ìi
ÀÅ
q ^ ^cbdegc&e8é êkÙ#é kÜÝÜJ zÀ û
`w6x(p$;zRÌÈ ² gìZ*~'=m}&·p'Zm
{*=m)à,=*p'qsmts
m{*
m ,}
.Zmv7m=x{zì7
Ç
{Ç
.=v7poNts/n$z7» 2oAm{Z;xsZmr*=tOx(qOZ* x(Zp$*tP¢p'qNZ*mtsZ tNm{
yRw$}
Ç
;z
ÁLª>Z*p
{p*zA¤ Tìw6*m{qz>lQ >Ì«w$*~*z 2
/z
[*~$ZZtO z K
z `qOm{/x(=
{m
Õ }\xsy´mr*=xsZp'¼À
º w$= z Tv*vim{qWìw$r*rZm·»GV¥'m{qz Tmo
Å Á
$Ç
û
ACS Paragon Plus Environment
$m{qOtsmn$z
The Journal of Physical Chemistry
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Page 22 of 30
à,=~*
û ²
~'m*m{qOZ
L*mx oXp$qs«oNVx(y¹
p'YvimxsZ*~
yRw$Zt{¼ª>y*mLx(qsw$*tsVx(=p'*tc¢qOp'
x(y*mL=*=xsfw$`txw6xsm
Þ xsp¹x(y*m|*Rw$txw6xsmHßÔ
{w$ÒimÄqsm8w6ZZm{rÃxsy*qsp$*~'yMx oApÔv*w6x(y/oXwntHoN=xsyMZ/xsm{qsm{rfw6xsmtOx(w6x(mt
æ/ç
û$ê8ë8ë8ëê å´ÁziïOðcÀ ñ é 'û ê{ë8ë8ëê í.Á>fw$im{=m{r´/n·Z*mcw$*r·qsm{r
{ZqO
{=m{t{zqOm{tsvim{
x(V¥'m{Vn'N¤\xTZtGw$tstO*m{r x(y*w6xQx(y*mJ*vv7mqv*w6x(y/oXwn ² y*w$tYp'qOmHtOx(w6x(mtxsyRw$¸x(ym´=poXmqQvRw6x(y/oXw8nÔã2z0b Çy{ e Ç3å ö íE¸ª>y*m À èWé
¢p'qoPw$qOrxsq(w$ts=xsZp'qsw6x(mtAw6qsmTw$tstOp
fw6xsm{roN=x(yYòLw$=p'*~)x(ymTvRw]x(y/oPw8n ²
oNy*Z=mNw$Zp$x(y*mq3xsq(w$ts=xsZp'
q(w]x(m{tGw$qOm~'=¥$m{J/nJÎ9
à,=~* ²
}
A7:9
`qOp'Rw$ZZVx n
âp'qcxsy*mHtOntx(m{
w$t[¢**
x(Zp$p6gx(ymN¥6w$qOfw$Zm
¢p'qvRw6xsy/oPw8n
²
@ G
û
éÉÎ 'ò¢p$q9x(y*mG*mx oAp'qOQtsy*poAm{rL=YàEZ~* ,ª>ymG*d7mqAp$7tOx(w6x(mt
w6*r¹ãÑw$qsmxw$6m{«w$tcå
Ì7:9
v*qOp'Rw$*=ZVx n
x(pÄqsm{w$
y¸x(y*mL|*Rw$Ptxw6xsmQß¼xsy*qsp'~'y¸Zp'~'m{qcvRw6x(y/oXw8n
é
aZtGr*m|R=x(V¥'m=nJfw6qs~'mqPx(yRw$
ZHxsy*mWw$=Jw$qOxsZ
Zm$
à,=~*
Å
q(w]x(m{tTò·¢p'q>Îé
w$*r¸ò¸é
x(ym
ÿ >ª>y*Zt9ÓO*tx(=|*m{tTxsy*m?
y*p'Z
mcp69x(y*=tTv*w$q(w$mxsm{qNtsmx
s mn91u
s mp;ku
Hw$*r
W¢p'qWx(ym¼tntOx(m
Þ p¥$m{qx(y*m´vRw6xsyoXw8n
²
x(pÍqsm{w$
y
p'qãw$twa¢*
x(=p'Ôp$x(ym
û 3ª>y*m*Kim{qGp$EtOxw]x(m{tGåw6*r·í¼w$qOmt(w$m?w$tN*tsmrZ´à,=~* XàRp'qGòHé
w8¥'mq(w$~'mAx(Zm3p ¥$m{q,xsy*mXv*w6x(y/oXwn ²
Õ
x(y*m´tOx(w6x(m
û
Õ zEqOm{tOv7m
x(V¥'m=n'JàRp'qÎÃé
² ¥'mq(w$~$m¼
p'*r*Vx(=p'Rw$G|RqstxO} v*w$tstsw$~'mÄx(=Ymt
x(ym´|R*w$NtOxw]x(mYß«tOx(w$qOxsZ*~a¢qsp'
à,=~*
W
ÿ zíÃé
x(ym
=tE
Zm8w6qs=n?tOWw$=Zmq;x(yRw$Kxsy*mPw8¥$m{q(w6~'mXx(=Ym3p¥'mq,x(y*mAvRw6xsyoXw8nQã2
y r9 xrn;
² Rw$VnxsZ
{w$w$rþw$vv*qsp8 ZYw6x(mqsm{Zw6x(=p'*tOy*Zv*tW7mx oXmm{
¸w$r
~'V¥'m{Í/n¹xsy*mHr*ZqOm{
xw$Rw$VnxsZ
{w$XtOp'ZxsZp'«p$dÀ /Ád*vip'Í
{p$Yv* x(Z~
Mw6*r
Ϫ>y*ma*fw6
ÃZ=*mµ=t Ò¥ ZwÄtsp'V¥ =*~µx(ym
{p$qsqsmtsvip'*r*=*~·w$tx(m{q)m¬Rw6x(=p';cª>y*mqsm{ra=Z*mcZt~'V¥'m¼/nµxsy*mw$v*vqsp8 ZYw6x(mKtOp'Z x(Zp$µr*m{qO=¥$m{r ¢qsp$
û
À Á,¤ Wxsy*Zt[|R~$*qsmNx(y*mT*mx oAp'qO¢qOp'
à,=~*
û
oNVx(yYå
é
ÿ z í´é
'
ACS Paragon Plus Environment
Õ zòHé
zw$*rWηé
û
À0qsw6x(mt
Page 23 of 30
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
The Journal of Physical Chemistry
Zaw6qs*Vx(q(w6qOn´**Vx(tÁGZt
p'*ts=r*m{qOm{r;cª>y*mQm =tOx(m*
{mp$
x
r*mv7m*r*tGp'´xsy*mq(w6xsm{t
à,=~* ÿ ²
û
Zt)wL*=¥'mqstsw$[v*qsp$v7mqOx n'z.p$*=n·=xst2¥6w$Z*m
~'m{*mqs=
c*mx oXp$qsJoN=x(y´x oXpY
{p'vimx(=*~
yRw$Zt2ts=Y=fw$qAx(pYxsy*m?*mx oAp'qs´tsyp oNÄ=àEZ~*
x,oNVx(yd=qsqOm¥'mqstOZ*=m3xsq(w$*tO=xsZp'*t.¢qOp'Êx(y*mAZ*Vx(Zw$'tOx(w6x(m Þ xspTxsy*mA|R*w$ txw6xsm9ß=dip$x(ycvRw6x(y/oXw8n t
\
à,=~*
Éà,ZqOtOxO}\vRw$tOt(w$~'mJx(=YmJv*qOp'Rw$ZZVx n¸r*m*tsVx(ZmtY¢qOp'
x oAp¿vRw]x(y*t ²
87:9pr9
*
`À Áz.
{p'v*xsm{rĢqsp$
x
Þ x(p¼x(y*m·tOxw]x(mLß¹xsy*qsp'~'y
w$rÂã¢p'qcx(y*mJZqOqsm¥'m{qOts=*ZmLmx oAp'qs¸tOy*poNÂ=Íà,Z~* ÿ «ª>ym´Z*mHw6*rÍqsm{rÔZ=*m{t
{p$qsqsmtsvip'*rx(px(y*mN¢**
x(Zp$*t
7%;krn;
x(y*m·tOxw]x(m
F
,À Áz
p'v*x(mrY¢qOp'
û x
û
[¬GÀ Å Ázw$Zp'~xsy*mGZp'*~$m{q`vRw6xsy ² z w6*r
[¬JÀ Õ Áz.w6Zp'*~Yx(y*mQtOy*p'qOxsm{qvRw6xsyaã2z;qOm{tsvim{
x(V¥'m{Vn'Kª>ymQK7mq)p$
tOx(w6x(mt2¢p'qGx oXpJvRw6xsy*t)w$qOmd~'V¥'mÄn·å
é ÿ
w$*rÄí¿é
Õ 2ª>y*mdx(qsw$*tO=x(=p'qsw6x(mtòÄé
*tOm{r;
$Å
ACS Paragon Plus Environment
z7οé
û
w$qOm
The Journal of Physical Chemistry
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
µ i
a1 µ λ µ µ b1 µ µ
a2
am
λ
µ
λ µ
µ
bn
b2 àEZ~'*qOm
Page 24 of 30
ûu
Õ
ACS Paragon Plus Environment
j
1 0.95
A
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
The Journal of Physical Chemistry
Probability U
Page 25 of 30
0.9 0.85 0.8 0.75 0.7 0.65 0.6 0.55 0.5 0
0.2
0.4
0.6
x = µ/λ
0.8
1
àEZ~'*qOm u
'ÿ
ACS Paragon Plus Environment
X
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Average time [1/µ]
The Journal of Physical Chemistry
15
[1/µ] [1/µ] λ=2
10
5
0 0
1
2
λ [µ]
3
4
5
àEZ~'*qOm Å u
d\
ACS Paragon Plus Environment
Page 26 of 30
0.1 0.09
s
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
The Journal of Physical Chemistry
Threshold time t
Page 27 of 30
0.08
Exact solution Approximation
0.07 0.06 0.05 0.04 0.03 0.02 0.01 0 0.5
0.6
0.7
0.8
0.9
Value of the probability θ
1
àEZ~'*qOm Õ u
|
ACS Paragon Plus Environment
The Journal of Physical Chemistry
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
a2 a1 i
am
λ
λ
λ µ b1
j µ
µ
Page 28 of 30
bn
b2
àEZ~'*qOm ÿ u
ACS Paragon Plus Environment
Page 29 of 30
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
The Journal of Physical Chemistry
!#"%$
&('
ACS Paragon Plus Environment
The Journal of Physical Chemistry
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
µ i
a1 λ µ µ b1
µ
a2
am
λ
µ
λ µ
µ
µ µ
bn
b2
W
àEZ~'*qOm
Å
u[ª ¶
Page 30 of 30
Î
W
ACS Paragon Plus Environment
j