EPR da Maksvell-Boltzman taqsimoti
Amalda, EPR namunalari alohida ajratilgan paramagnit markazlardan emas, balki ko'plab paramagnit turlarining to'plamlaridan iborat. Agar radikallar populyatsiyasi termodinamik muvozanatda bo'lsa, uning statistik taqsimoti Boltsman taqsimoti bilan tavsiflanadi:
n
upper
n
lower
=
exp
(
−
E
upper
−
E
lower
k
T
)
=
exp
(
−
Δ
E
k
T
)
=
exp
(
−
ϵ
k
T
)
=
exp
(
−
h
ν
k
T
)
{\displaystyle {\frac {n_{\text{upper}}}{n_{\text{lower}}}}=\exp {\left(-{\frac {E_{\text{upper}}-E_{\text{lower}}}{kT}}\right)}=\exp {\left(-{\frac {\Delta E}{kT}}\right)}=\exp {\left(-{\frac {\epsilon }{kT}}\right)}=\exp {\left(-{\frac {h\nu }{kT}}\right)}}
bu yerda
n
upper
{\displaystyle n_{\text{upper}}}
- yuqori energiya holatini egallagan paramagnit markazlar soni,
k
{\displaystyle k}
Boltsman doimiysi va
T
{\displaystyle T}
termodinamik haroratdir . 298 K da, X diapazonli mikroto'lqinli chastotalar (
ν
{\displaystyle \nu }
≈ 9,75 GHz) beradi
n
upper
/
n
lower
{\displaystyle n_{\text{upper}}/n_{\text{lower}}}
≈ 0,998, ya'ni yuqori energiya darajasi pastroqdan bir oz kichikroq aholiga ega. Shu sababli, pastdan yuqori darajaga o'tish teskarisiga qaraganda ko'proq ehtimoli bor, shuning uchun energiyaning aniq yutilishi mavjud.
EPR usulining sezgirligi (ya'ni, aniqlanadigan aylanishlarning minimal soni
N
min
{\displaystyle N_{\text{min}}}
) foton chastotasiga bog'liq
ν
{\displaystyle \nu }
ga binoan
N
min
=
k
1
V
Q
0
k
f
ν
2
P
1
/
2
,
{\displaystyle N_{\text{min}}={\frac {k_{1}V}{Q_{0}k_{f}\nu ^{2}P^{1/2}}},\qquad }
bu yerda
k
1
{\displaystyle k_{1}}
doimiy hisoblanadi,
V
{\displaystyle V}
namuna hajmi,
Q
0
{\displaystyle Q_{0}}
mikroto'lqinli bo'shliqning (namuna kamerasi) yuklanmagan sifat omilidir,
k
f
{\displaystyle k_{f}}
bo'shliqni to'ldirish koeffitsienti va
P
{\displaystyle P}
spektrometr bo'shlig'idagi mikroto'lqinli quvvatdir. Bilan
k
f
{\displaystyle k_{f}}
va
P
{\displaystyle P}
doimiy bo'lish,
N
min
{\displaystyle N_{\text{min}}}
~
(
Q
0
ν
2
)
−
1
{\displaystyle (Q_{0}\nu ^{2})^{-1}}
, ya'ni,
N
min
{\displaystyle N_{\text{min}}}
~
ν
−
α
{\displaystyle \nu ^{-\alpha }}
, qayerda
α
{\displaystyle \alpha }
≈ 1,5. Amalda,
α
{\displaystyle \alpha }
spektrometr xususiyatlariga, rezonans sharoitlariga va namuna hajmiga qarab 0,5 dan 4,5 gacha o'zgarishi mumkin.
Shuning uchun past aniqlash chegarasi bilan katta sezuvchanlik olinadi
N
min
{\displaystyle N_{\text{min}}}
va katta miqdordagi aylanishlar. Shunday qilib, kerakli parametrlar:
uz.wikipedia.org