X m i c e l l e = X N N {\displaystyle X_{micelle}={\frac {X_{N}}{N}}} X 1 {\displaystyle X_{1}} C = X 1 + X N {\displaystyle C=X_{1}+X_{N}\ }
X 1 = ( C − X 1 N ) 1 / N e − ( μ 1 0 − μ N 0 ) / k T {\displaystyle X_{1}=\left({\frac {C-X_{1}}{N}}\right)^{1/N}e^{-\left(\mu _{1}^{0}-\mu _{N}^{0}\right)/kT}}
X N = N [ X 1 e ( μ 1 0 − μ N 0 ) / k T ] N {\displaystyle X_{N}=N\left[X_{1}e^{\left(\mu _{1}^{0}-\mu _{N}^{0}\right)/kT}\right]^{N}}
C C M C = 2 N 1 / ( N − 1 ) K N / ( N − 1 ) {\displaystyle C_{CMC}={\frac {2}{N^{1/(N-1)}K^{N/(N-1)}}}}
K = e ( μ 1 0 − μ N 0 ) / k T {\displaystyle K=e^{\left(\mu _{1}^{0}-\mu _{N}^{0}\right)/kT}}
X = 1 A p a r t i c l e {\displaystyle X={\frac {1}{A_{particle}}}}
P = k T N [ C + ( N − 1 ) X 1 ] {\displaystyle P={\frac {kT}{N}}\left[C+(N-1)X_{1}\right]}
π = k T N [ 1 ( A − A 0 ) + ( N − 1 ) ( A 1 − A 0 ) ] {\displaystyle \pi ={\frac {kT}{N}}\left[{\frac {1}{(A-A_{0})}}+{\frac {(N-1)}{(A_{1}-A_{0})}}\right]}
( A 1 − A 0 ) = ( A − A 0 ) [ 1 + ( 2 ( A c − A 0 ) A 1 − A 0 ) N − 1 ] {\displaystyle (A_{1}-A_{0})=(A-A_{0})\left[1+\left({\frac {2(A_{c}-A_{0})}{A_{1}-A_{0}}}\right)^{N-1}\right]}
E = E i n t + E d i s p + P A {\displaystyle E=E_{int}+E_{disp}+PA\ }
K c Δ R ( θ , c ) = 1 M w P ( θ ) + 2 A 2 c = 1 M w ( 1 + q 2 R g 2 3 ) + 2 A 2 c {\displaystyle {\frac {Kc}{\Delta R(\theta ,c)}}={\frac {1}{M_{w}P(\theta )}}+2A_{2}c={\frac {1}{M_{w}}}\left(1+{\frac {q^{2}R_{g}^{2}}{3}}\right)+2A_{2}c}
![{\displaystyle X_{N}=N\left[X_{1}e^{\left(\mu _{1}^{0}-\mu _{N}^{0}\right)/kT}\right]^{N}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/802fe566de8c0dfe615d7ca0aff1b0815edc6969)
![{\displaystyle P={\frac {kT}{N}}\left[C+(N-1)X_{1}\right]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d3896e4de14102f557045e11bbef858b2edf3522)
![{\displaystyle \pi ={\frac {kT}{N}}\left[{\frac {1}{(A-A_{0})}}+{\frac {(N-1)}{(A_{1}-A_{0})}}\right]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b70672c4eff50d5a6cc03da5d573c5ab7cdd6eac)
![{\displaystyle (A_{1}-A_{0})=(A-A_{0})\left[1+\left({\frac {2(A_{c}-A_{0})}{A_{1}-A_{0}}}\right)^{N-1}\right]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a28359faf946205764e7caeda9d49f8b105d95ec)
