Diffusion and trapping in dendrimer structures

We investC"- di#usion on models of large moleculeswit dendrimerstrimerM' The models we use aretMEBzzEMC' Cayley tyley We focus on di#usionpropertz8z such as tM excursion distsionts mean squaredisplacement of tM di#using partngM--B and td area probed, as given by tM random walkparamet-- S N ,t' number of tMdistz-' sitvisitzFinally we lookat t tkMz'z kinet'z for randomlydistlyM`--' sttlyM`-- ttt of lowconcentMC`]--8z We use di#erent coordinatC` numbers, z, anddi#erent generatMC orders g of a dendrimerstrimerM' We show tow for calculatE ][ on dendrimers where wesimulat tm entla stlatM t finit sizee#ect dominat makingtk result worttEB` We,t]8]EMC`[ implementE tm algoritt tlg donot ret8` tt underlying sterlying and tdM e#ectBzMC te random walk is performed on anequivalent infinit stitlent We find a universal linear behavior for all tl propert'M examined,tmi di#ering fromto regularlatlarM` The averagedisplacement R grows linearlywit tta implyingtpl grows as t 2inst-M of t. The S also grows linearlywit tta which resemblests random walk case in t]-]]MC"zz-Mtt lat`zz-M but wit adi#erent prefact whichstchM'E depends on z. Trapping is dependent on S N , as expectMC and follows exactsit behavior. Duet te nat`] oftM'B stB--8]MC` tt random walk is indeed at--E of a "biased" walk. We devise a model in which wetM` out tt "bias"facts' and intME model we show tho th systM becomes di#usive innat--8' i.e.te mean squaredisplacement is linearwit tta Theseresult could be utME][8 if one is t design a dendrimersysti wit specifically desiredpropertz8E # 2002 Elsevier Science B.V. All right reserved. 1.I oduction Di#usionpropert ies onstzB tzB wit Cayley tyM tyM`B---- haverecent lyatz[`--` d a considerable intM est mainly because of tM newsyntzB is of dendrimer molecules [1--8],t--8 bec..