Context : Various studies have emphasized variations of the charge state and composition of the interstellar polycyclic aromatic hydrocarbon ( PAH ) population in photodissociation regions ( PDRs ) .
These changes are expected to impact the energetics and chemistry in these regions calling for a quantitative description .

Aims : We aim to model the spatial evolution of the charge and hydrogenation states of PAHs in PDRs .
We focus on the specific case of the north-west ( NW ) PDR of NGC 7023 , for which many observational constraints are available .
We also discuss the case of the diffuse interstellar medium ( ISM ) .

Methods : The physical conditions in NGC 7023 NW are modelled using a state-of-the-art PDR code .
We then use a new PAH chemical evolution model that includes recent experimental data on PAHs and describes multiphoton events .
We consider a family of compact PAHs bearing up to 96 carbon atoms .

Results : The calculated ionization ratio is in good agreement with the observed ratio in NGC 7023 NW .
Within the PDR , PAHs evolve into three major populations .
We find medium-sized PAHs ( 50 \lesssim N _ { C } \lesssim 90 ) to be normally hydrogenated , while larger PAHs ( N _ { C } \gtrsim 90 ) can be superhydrogenated , and smaller species ( N _ { C } \lesssim 50 ) are fully dehydrogenated .
In the more diffuse gas of the cavity , where the fullerene C _ { 60 } was recently detected , all the studied PAHs are found to be quickly fully dehydrogenated .
PAH chemical evolution exhibits a complex non-linear behaviour as a function of the UV radiation field because of multiphoton events .
Steady state for hydrogenation is reached on timescales ranging from less than a year for small PAHs , up to 10 ^ { 4 } years for large PAHs at A _ { V } =1 .
Critical reactions that would need more studies are the recombination of cations with electrons , the reactivity of cations with H _ { 2 } and the reactivity of neutral PAHs with H .

Conclusions : We developed a new model of PAH chemical evolution based on the most recent available molecular data .
This model allows us to rationalize the observational constraints without any fitting parameter .
PAHs smaller than 50 carbon atoms are not expected to survive in the NGC 7023 NW PDR .
A similar conclusion is obtained for the diffuse ISM .
Carbon clusters turn out to be end products of PAH photodissociation , and the evolution of these clusters needs to be investigated further to evaluate their impact on the chemical and physical evolution of PDRs .