$A$	active area/m2
$A_f$	wet area/m2
$a_f$	specific surface area of hydrated tubes/m−1
$a$	humidification coefficient/–
$C$	constant in Equation (10)/m−3
$C_{H^{+}}$	proton concentration/mol m−3
$D_{H^{+}}$	proton diffusivity/m2 s−1
$DS$	degree of sulfonation/–
$d_o$	dry characteristic spacing/m
$d_c$	average distance between tubes/m
$F_v$	fractional free volume/–
$f\left(R\right)$	void radius probability density function/–
$g\left(V\right)$	volume probability density function/–
$I$	relative intensity, current density/–, A m−2
$IEC$	ion exchange capacity/eq kg−1
$L$	length/m
$N_{H^{+}}$	proton flux/mol m−2 s−1
$N_t$	total count/–
$n$	number of PSU structural units/–
$n_A$	number of ionic tubes per unit of geometric area/m−2
$n_{\tau }$	tortuosity exponent/–
$M$	mass/kg
$m$	number of PPSU structural units/–
$R$	mean hole radius/m
$R_m$	ionic resistance/Ω
$\mathrm{RH}$	relative humidity/–
$r$	radius of ionic tubes/m
$SW$	swelling ratio/–
$T$	temperature/K
$t$	time/s
$V$	volume/m3
$WU$	water uptake/–
$w$	weight function/–
$x$	coordinate across PEM thickness/m
Greek letters
$\alpha$	relative intensity/–
$\beta$	thermal expansion coefficient/K−1
$\delta$	PEM thickness/m
${\epsilon }_w$	average water-filled porosity/–
$\rho$	density/kg m−3
$\kappa$	proton conductivity/S m−1
$\lambda$	annihilation rate/s−1
$\mu$	dynamic viscosity/kg m−1 s−1
σ	standard deviation, average charge density/m, C m−2
$\tau$	lifetime component/s
${\varphi }_v$	water volume fraction/–
${\varphi }_w$	volume fraction of hydrated tubes/–
${\varphi }_{wr}$	relative volume fraction of hydrated sites/–
$\phi$	potential/V
$\chi$	mute variable in Equation (15)
Subscripts
$c$	characteristic
$dry$	dry conditions
$fh$	fully humidified
$h$	hydrated
$th$	threshold
$w$	water
$wet$	wet conditions
Superscripts
$avg$	average
$eff$	effective
$f$	fluid phase
$n$	number of lifetime components
$ref$	reference conditions