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functional soft materials composed of many nano - particles often appear in complex structure both as 2-dimensional films @xcite and 3-dimensional super - crystal structures @xcite .
these structures emerge in various _ processes of self - assembly _ , most of which utilize liquid degrees of freedom and nonequilibrium methods @xcite .
the gold nanoparticles are often used due to the property that their surfaces can be _
functionalized _ in an appropriate manner .
the functionalization of the nanoparticle surfaces has effects on their interactions @xcite . in the case of nanoaprticle films on substrate assembled by the liquid evaporation @xcite the thiol - passivated nanoparticles where used , where the attached chains determine the minimum distance between two neighbouring nanoparticles .
another way to induce desired interaction between two nanoparticles was designed recently with attaching the pieces of biologically compatible strands of dna molecules to different nanoparticles @xcite .
the dna - mediated interaction then utilizes the _ biological recognition _ and binding energy of the compatible dna base pairs . depending on the number of other factors , which we will also discuss later
, this programmable self - assembly may lead to random as well as regular super - crystal structures , as shown in recent experiments in refs .
@xcite . somewhat similar ( but in a different potential range ) , is the bio - recognition assembly which utilizes biologically compatible protein molecules , for instance the antigen 
antibody recognition @xcite , which can be used in biosensors .
the nanoparticle assemblies exhibit a wide range of physical properties which are not found in the bulk materials and at the level of a single nanoparticle @xcite .
moreover , the emergent physical properties of the nanoparticle assemblies can often be related to their spatial structure @xcite .
for instance , new optical and magnetic properties have been found in super - lattices made of nanocrystal @xcite . by speciffic functionalization of their surfaces
gold nanoparticles develop directionally dependent exchange interaction @xcite . assuming that such nanoparticles can be arranged on nodes of a sparse scale - free graph
, numerical simulations predict new features of the magnetic response of such a structure @xcite , compared to the classical memory materials @xcite . similarly , the films of gold nanoparticles under voltage bias conduct current via _ single - electron tunneling
_ processes @xcite due to their small capacitances and the coulomb blocade effects @xcite .
in contrast to classical conduction , the single - electron conduction processes have numerous advantages , e.g. , the absense of dissipation due to heathing , and the nonlinear current - voltage characteristics , which are important in the nanoelectronics . experimentally a large nonlinearity of the current  voltage curve has been found in self - assembled nanoparticle films on substrates , which appears to be fairly correlated with the film structure @xcite .
the random structure of nanoparticle films on substrates can be adequately modelled by planar graphs ( _ nano - networks _ ) @xcite . for the charge transport via single - electron processes , which we study here , the topological elements of these nano - networks are suitably selected as follows : the _ nodes _ represent nanoparticles , whereas _ edges _ ( links ) are the tunneling junctions between two nanoparticles .
for the junction ( link ) to occur between two nanoparticles , the distance between them must be smaller than the _ tunneling radius _ of the electrons for that kind of nanoparticles @xcite .
the charge transport through the film under applied voltage can be described within the model of the capacitively - coupled nanoparticles on substrate @xcite . in our previous work @xcite we generalized the model of capacitively - coupled nanoparticle assemblies for an arbitrary topology of the nano - networks @xcite and implemented a numerical model of single - electron tunnelings driven by the external voltage through such networks .
theoretical background and the details of the numerical implementation is reviewed in ref .
the simulation results revealed the topology - induced nonlinearity in the @xmath0 curve , in a good agreement with the experiments @xcite .    in the present work we study the collective dynamic behavior which makes the physical basis for the observed @xmath0 nonlinearity , in particular , the long - range correlations in charge fluctuations monitored at each nanoparticle and inhomogeneous charge flow along the conducting paths through the sample and at the electrode .
we determine the probability distributions of various quantities related to the conduction process and demonstrate how the topological and charge disorder affect the quantitative statistical properties and the @xmath0 dependences .
the organization of the paper is as follows : in section  2 we present the model of the particle self - assembly with bio - recognition bonding and show some of the typical emergent structures . in section  3
we summarize the theoretical background of the conduction with single - electron processes and its numerical implementation for an arbitrary network topology .
the visualization of the conduction paths through two network types , the regular and inhomogeneous nanoparticle aggregates , as well as the statistical properties of the topological and charge flow are shown in section  4 . in section  5
we analyse the simulated time series of charge and current fluctuations and the related @xmath0 curves .
section  6 gives a short summary of the results .
different assembly processes make use of the liquid phase , that provides the nanoparticle diffusion and affects the interaction .
the assembly with fast evaporation of the liquid @xcite induces additional constraints to the particle motion and interaction .
the interaction itself between pairs of the nanoparticles moving in a liquid is taking part at short distances and depends on the type of functionalization of their surfaces , as mentioned above . in the case of bio - recognition binding , which we will discuss shortly here ,
the attached dna induce the differences between two types of nanoparticles , i.e. , type a and type b nanoparticles , each of which carry the biologically compatible strand of the same dna molecule .
thus , the interaction between a  b type is attractive within some bonding distance @xmath1 .
the bonding distance depends on the lengths of the attached molecules and on the number of the compatible base - pairs on them @xcite .
therefore , it exceeds the sum of the particle radii @xmath2 . the effective interaction between a 
b particles can be then modeled by the lennard - jones potential @xcite @xmath3 where @xmath4 is the actual distance between particles and the potential minimum corresponds to the optimal bonding distance . in the present case ,
the parameters @xmath5 and @xmath6 depend , roughly speaking , on the lengths of the attached dna chains and the strength of binding ( number of the compatible base pairs)@xcite . on the contrary , the particles which carry biologically incompatible dna strands have no attractive interaction of this type . the repulsive part alone of the potential in eq .
( [ eq - ljpotential ] ) can describe the interaction of the equal - type particles a  a and b  b , occurring at short distances .    [
cols="^,^ " , ]     the correlations in the current fluctuations at the electrode , i.e. , at the last layer of the nanoparticles connected to the electrode , are caused by the tunneling processes deeper in the sample .
the time - series of the number of tunnelings \{@xmath7 } at all nanoparticles in in the whole network and their power spectra are shown in fig .
[ fig - nt ] .
the power spectrum of the number of tunnelings exhibits long - range correlations for high frequencies , according to @xmath8 the exponent @xmath9 ( within numerical error bars ) for the topologically disordered nano - network nnet1 , suggesting strong cooperation between the conducting paths .
whereas , the correlations are much weaker in the triangular array , leading to @xmath10 for high frequencies , and the absence of correlations at low frequencies .
in our numerical study of the conducting nanoparticle films on substrates , we pointed out several steps that play an important role in designing the conduction properties of the films . specifically , we study in quantitative details the emergent properties of such nanoparticle assemblies along the line from the self - assembly processes , the topology of structures , and conduction through such structures .    *   _ self - assembly _ processes are leading to different types of structures of the film .
we have shown that both regular and highly inhomogeneous nanoparticle films , which are typically fabricated in entirely different techniques@xcite , can be assembled within the same process with the bio - recognition binding and varying a single control parameter .
*   _ conducting paths _ through the film have been identified and their topological centrality and the dynamical flow computed for for @xmath11 .
coalescence of flow along different paths contributes to the nonlinear @xmath0 dependences in a range of voltages above the transition @xmath12 . in our simulations ,
the nonlinearity exponent @xmath13 depends strongly on the structure , in agreement with measured @xmath14 curves in different nanoparticle films @xcite . *   _ collective dynamical effects _ in the tunneling processes deep inside the sample lead to the non - gaussian current fluctuations at the electrode .
we have determined various statistical measures of these collective effects .
in particular , we find the long - range correlations in charge fluctuations at all nanoparticles , broad distribution of flow on junctions through the nano - network , and non - gaussian distribution of the current increments on the electrode . a non - gaussian distribution have been found in the experiments with nanowires @xcite .
our numerical results suggest that @xmath15-gaussian distribution with different parameters could be measured in the nanoparticle films .
the occurrence of the @xmath15gaussian in a larger class of complex dynamical systems with long - range interactions has been discussed recently @xcite .
furthermore , we demonstrate how different types of disorder affect the conduction in our comparative study of the regular nanoparticle array in the presence of local charge disorder , on one side , and the topologically inhomogeneous nano - network without charge disorder , on the other .
we hope that our detailed numerical study of the processes leading to different structures and the structure - dependent function of the nanoparticle assemblies sheds a new light on the problem of engineering of the functional materials with desired characteristics .
we thank the project mrtn - ct-2004 - 005728 ( ec ) and the program p1 - 0044 ( slovenia ) for the support .
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using numerical modeling we study emergence of structure and structure - related nonlinear conduction properties in the self - assembled nanoparticle films . 
 particularly , we show how different nanoparticle networks emerge within assembly processes with molecular bio - recognition binding . 
 we then simulate the charge transport under voltage bias via single - electron tunnelings through the junctions between nanoparticles on such type of networks . 
 we show how the regular nanoparticle array and topologically inhomogeneous nanonetworks affect the charge transport . 
 we find long - range correlations in the time series of charge fluctuation at individual nanoparticles and of flow along the junctions within the network . 
 these correlations explain the occurrence of a large nonlinearity in the simulated and experimentally measured current - voltage characteristics and non - gaussian fluctuations of the current at the electrode .