the functionalization 
 of a surface with polyelectrolyte multilayers 
 ( pems ) via layer - by - layer assembly allows the tailoring of surface 
 charge and hydrophobicity .
thus , pem - modified surfaces 
 have been shown to exhibit antifouling properties , and allow for surfaces 
 with variable charge densities .
the assembly of such films is simple , involving only the alternating 
 deposition of polycations and polyanions , yet adjusting several key 
 parameters during assembly allows precise control of the nanoscopic 
 structure of the resulting films .
these parameters include the number 
 of layers , the ph and the ionic strength of the deposition solutions , 
 and the selection of the polyelectrolytes themselves .
for instance , using assembly solutions in which the polyelectrolytes 
 are not fully ionized results in thicker layers and rougher surface 
 topology than those made with fully ionized polyelectrolytes . when multilayers are constructed using 
 weak polyelectrolytes , their 
 topographical and electronic characteristics
ph affects the dissociation of weak polyelectrolytes , 
 and thus tunes the charge density at the film - solvent interface . as a result
, the ratio of positive to negative charge near the surface 
 of a pem film incorporating one or more weak polyelectrolytes can 
 be tuned by adjusting the ph of the solution , and this charge ratio 
 determines not only the electrostatic character of the film , but the 
 nanoscale structure of the film itself . in previous 
 research
we have shown that changing the degree of ionization of a 
 weak polyelectrolyte brush allows for reversible and charge - selective 
 sequestration of probe molecules , which 
 supports their use in drug release applications .
an understanding of the interfacial transport mechanisms that 
 occur 
 within and near these charged and crowded interfaces could help realize 
 the broad application of polyelectrolyte films .
recent work has demonstrated 
 that transport within and near complex environments such as polyelectrolyte 
 films can not be described by traditional brownian diffusive models .
anomalous diffusion in a polyelectrolyte film can be attributed 
 to confinement of isolated water channels and pockets within the film 
 or hopping from one polyelectrolyte site to another .
the transport of small molecules within the 
 film may also be coupled to the motion of the polyelectrolyte chains 
 themselves .
studies that focus specifically 
 on pem films have found that using a single diffusion coefficient 
 is not adequate to describe the observed transport .
additionally , the rate of diffusion was found to depend 
 on the distance of the probe from the surface of the film .
this is attributed to the fact that the outermost 
 layers are not as compact as the inner bulk of the film .
studies of the dynamics of protein transport on or in a pem using 
 fluorescence response after photobleaching ( frap ) have shown that 
 the diffusion coefficient and the mobile fraction of the adsorbed 
 protein are dependent on the concentration of the guest molecules 
 and the chemistry of the outermost polyelectrolyte layer .
fluorescence imaging , especially single molecule tracking , 
 enables 
 the direct observation of the dynamics of molecules at interfaces 
 and near or within thin films .
previous research on transport in polyelectrolytes has indicated 
 that diffusion within polymer films is heterogeneous and that single 
 molecule measurements are required to determine the mechanistic detail 
 of rotational and translational dynamics .
found evidence that solute hopping plays a role in 
 the diffusion of charged probes within a poly(styrene sulfonate ) brush 
 film using polarization resolved fluorescence correlation spectroscopy 
 ( fcs ) .
an fcs study on diffusion in multilayers 
 composed of poly(styrene sulfonate ) and poly(diallyldimethylammonium 
 chloride ) found that transport could be described by reversible adsorption / desorption 
 events , as well as confined diffusion .
for uncharged probe molecules , two distinct adsorption components 
 were required to adequately model the data , but when a charged probe 
 molecule was used , only one was required ; however , charged molecule 
 diffusion was not discussed in detail . additionally , the autocorrelation analysis used reflects ensemble 
 dynamics determined from a model , not direct observation .
the dependence 
 of transport dynamics in pems on probe charge and solution ph remains 
 unexplored .
we report on the transport of anionic and cationic 
 probe molecules 
 at a variety of ph values in a pem , layer - by - layer assembled from 
 the weak polycation poly(allylamine hydrochloride ) ( pah ) and the weak 
 polyanion poly(acrylic acid ) ( paa ) measured using single molecule 
 fluorescence microscopy .
we performed particle tracking on six different 
 probe / condition pairs : alexa 555 , an anionic probe , as well as rhodamine 
 6 g ( r6 g ) , a cationic probe , at ph 3.5 , 5.7 , and 8.7 .
the average number 
 of events per frame was used to demonstrate the ph and charge dependence 
 of probe association with the film .
radius of gyration evolution analysis 
 was used to illustrate the multimodal characteristics of the trajectories . 

we then extracted quantitative information from the trajectories using 
 the single frame displacement distributions and the diffusion coefficient 
 distributions .
our results demonstrate that molecules undergo reversible 
 adsorption to the pem , as well as hopping .
the degree of association 
 and the presence of confined diffusion is found to depend on the ph 
 of the dye solution and charge of the probe molecules used .
first , the no . 1 
 borosilicate glass coverslips ( 22  22 mm , vwr ) were sonicated 
 sequentially for 15 min each with water , acetone , and water . the substrates 
 were then treated with piranha solution ( 70% h2so4 and 30% h2o2 ) for 30 min .
the substrates were 
 washed with water to completely remove the piranha solution , dried 
 with compressed air , and then cleaned with oxygen plasma for 3 min . 

the substrates were immersed in 0.5 vol % aminopropylsilane ( aps , 
 sigma ) in dry toluene for 2 h. after washing the substrate with toluene 
 and drying it with compressed air , the functionalized substrate was 
 immersed in 0.1 m hcl for at least an hour .
one milligram per milliliter 
 of paa ( mw = 1800 , sigma ) solution was used as the negatively charged 
 polyelectrolyte solution , while 1 mg / ml of pah ( mw 120,000200,000 , 
 sigma ) was used as the positively charged polyelectrolyte solution . 

the ph of the paa and the pah solutions were adjusted to 3.5 and 7.5 
 by adding 0.1 m hcl or 0.1 m naoh , respectively .
the aps - functionalized 
 substrate was immersed in paa solution for 15 min , water for 1 min , 
 pah solution for 15 min , and water for 1 min .
this cycle was repeated 
 until the desired number of bilayers was achieved . for this work , 
 10 and
multilayer thickness was measured using ellipsometry ; 
 see the supporting information ( si ) for 
 details .
solutions of the probe molecules 
 were prepared by diluting rhodamine 6 g ( cationic , sigma ) or alexa 
 fluor 555 ( anionic , invitrogen ) to 10 pm in molecular biology grade 
 water ( ph 5.7 , thermo scientific ) .
hcl ( ph 3.5 , sigma - aldrich ) and 
 tris buffer ( ph 8.7 , sigma - aldrich ) were used to adjust aqueous ph .
samples were analyzed using 
 a custom - built total internal reflection wide field fluorescence ( tirf ) 
 microscope .
a 532 nm diode laser ( coherent , compass 315m-100sl ) was 
 used for excitation .
excitation light was expanded and passed to an 
 oil immersion objective ( 1.45 na , 100 , alpha plan - fluar , carl - zeiss ) 
 through a dichroic mirror ( chroma , z532/633rpc ) .
the beam was focused 
 to the edge of the objective such that the angle of incidence on the 
 sample was 79 resulting in through - the - objective tirf . 

all measurements were conducted with an excitation power 
 density of 1.3 mw / cm .
fluorescence emission from the sample 
 was collected through the same objective ( epifluorescence ) and separated 
 from excitation light by the dichroic mirror , as well as a notch filter 
 ( kaiser , hnpf-532.0 - 1.0 ) and a bandpass filter ( chroma , et585/65 m ) . 

emission light was collected using an emccd camera ( andor , ixon 897 ) 
 using an integration time of 30 ms and an em gain of 300 .
the recovery 
 time of the camera was 32 ms , resulting in a total time of 62 ms between 
 frames .
a drop of probe solution was added to a multilayer sample 
 and allowed to equilibrate for 20 min to ensure complete hydration 
 of the multilayer prior to measurement .
the raw data from 
 the emccd detector was analyzed as a series of two - dimensional images . 

briefly , our program first increases the signal - to - noise 
 ratio ( snr ) of each frame by convolution between the frame and a 3 
  3 matrix of ones .
this step has been found to be important 
 in tracking algorithms , and increases the snr by 2 to 3 times .
the corresponding local intensity threshold 
 was set to the local background plus three times the standard deviation 
 of local noise .
next , the centers of 
 all the preidentified particles were calculated using a radial symmetry 
 algorithm .
the second moment of the particle 
 is compared with the second moment of the same fitting region with 
 gaussian noise .
only if the second moment of the particle is smaller 
 than 90% of the second moment of the gaussian noise will we consider 
 the particle a real particle and record its position .
finally , we 
 used a nearest neighbor algorithm to generate molecular trajectories . see the si for a sample of raw data ( file 
 la5012007_si_001.avi ) and the same data overlaid with tracking results 
 ( file la5012007_si_002.avi ) .
we measured trajectories of cationic r6 g and anionic alexa 555 
 diffusing on the surface of a 10 bilayer paa / pah multilayer in molecular 
 biology grade water ( ph 5.7 ) , hcl ( ph 3.5 ) , and tris buffer ( ph 8.7 ) . 

we begin with a discussion of the ionization state of the probes and 
 film at the different ph conditions as this is crucial to the interpretation 
 of the results .
the degree of interaction of the probe molecules is 
 used to show the ph - dependence of the interaction of the probe molecules 
 with the multilayer .
radius of gyration evolution analysis is used 
 to determine that under certain probe - condition combinations transport 
 is characterized by intermittent surface adsorption .
analysis of the 
 single frame displacement and diffusion coefficient histograms is 
 used to further characterize the tunability of film interaction for 
 the various probe - condition pairs .
finally , these results are used 
 to develop an interaction mechanism based on electrostatic interactions 
 of the probes with the outermost layer of the film . the charge density at the interface 
 changes with the ph value of the solution during film assembly and 
 during the measurements . work by rubner and others has demonstrated 
 that the pka of a polyelectrolyte can 
 be shifted by up to four ph units when the polyelectrolytes are incorporated 
 into a multilayer compared to the pka in 
 solution . according to their measurements , in our 
 hcl solutions ( ph 3.5 ) paa
should be approximately 87% ionized while 
 pah should be close to 100% ionized . in mb water ( ph 5.7 )
paa becomes 
 slightly more ionized 90% while pah remains nearly completely 
 ionized . in tris buffer ( ph 8.7 )
paa becomes still more ionized reaching 
 > 90% ionization while pah becomes slightly less ionized 90% . 

it should be noted that the actual degree of ionization values post 
 assembly are difficult to quantify as they not only depend on the 
 chosen polyelectrolyte pair , but the assembly ph of the polymer solutions .
the inner layers of the film are uncharged due 
 to the intrinsic charge compensation that holds the multilayer together .
because the pah is part of a multilayer , most 
 of the charge in the outermost layer will be compensated by the underlying 
 paa layer , but we expect some positive charge to remain to facilitate 
 the charge overcompensation mechanism that is essential for multilayer 
 assembly .
alexa 555 is a 
 strong acid based on its sulfonate functional groups and as such , 
 all of the molecules are negatively charged under all three conditions . 

the pka of r6 g is 7.5 , so the molecules are fully ionized ( positively charged ) 
 at ph = 3.5 , 60% ionized at ph = 5.7 and 6% ionized at ph = 8.7 .
( a ) molecular structures of pah , 
 ( b ) paa , ( c ) r6 g , and ( d ) alexa 568 .
the refractive indices of water , polymer 
 film , glass substrate , and objective oil are also shown .
the molecular structure of the probe molecules 
 ( alexa 568 instead 
 of alexa 555 because the structure of alexa 555 is proprietary ) as 
 well as those of paa and pah are shown in figure 1 ( a , b , c , and d ) .
because of the excitation geometry and 
 integration time of 30 ms , probes diffusing freely in solution ( d  10 nm / s ) are visible only as a constant background signal and are 
 therefore not counted during particle identification .
probes adsorbed in the film bulk will bleach a short time 
 after the sample is illuminated .
most of the events , therefore , are 
 new molecules associated with the film surface that subsequently either 
 diffuse back into solution or remain within the film until they photobleach . 
 in order to verify that the algorithm is correctly linking trajectories , 
 the order of the frames from 1000 frames worth of experimental data 
 was randomly shuffled , and the data was 
 reanalyzed , producing only 44 trajectories greater than the 5 frame 
 cutoff used for analysis , compared to 1248 trajectories for the unshuffled 
 data .
this result suggests that erroneous linking of different molecules 
 is rare ( < 4% false positives ) .
based on previous studies and our experimental 
 design , the molecules we observe are expected to be probe molecules 
 interacting with the outermost layers of the polymer film as depicted 
 in the experimental cartoon in figure 1e .
intensity 
 measurements confirm that the tirf condition occurs at the film water 
 interface as depicted in figure 1e .
while we can not rule out observation 
 of diffusion within the film bulk , adsorption of probe molecules in 
 a pem has been shown to be dependent on salt concentration .
have reported that residual 
 salt is only found in the outermost layer of the pem , which strongly 
 suggests that we are observing probe interaction near the outer interface 
 of the pem . the strongest probe 
surface 
 interaction exists for alexa 555 in hcl and r6 g in tris buffer ( figure 2a and 2 g ) .
the number of 
 events per frame was calculated by averaging the number of new objects 
 appearing per frame .
for alexa 555 , there is a decrease in probe association 
 when ph is increased , from an average of 10  4 events per frame 
 in hcl , to 1  1 in mb water , and 2  1 in tris buffer ( figure 2d ) .
generally , the opposite is true for r6 g ( figure 2h ) . as the ph
is decreased , there is somewhat less 
 association of r6 g with the film , from an average number of events 
 per frame of 7  3 in tris to 5  2 in mb water to 2  
 2 in hcl , although the distributions overlap considerably ( figure 2d ) .
( a , b , c ) 50 frames of trajectories measured in the same 
 area for 
 alexa 555 over the 10 bilayer film in hcl , mb water , and tris buffer , 
 respectively .
( e , f , g ) 50 frames of trajectories measured in the same 
 area for r6 g over the 10 bilayer film in hcl , mb water , and tris buffer , 
 respectively .
( d , h ) histograms showing the number of particles identified 
 per frame for alexa 555 and r6 g respectively for the various conditions 
 along with the average number of events per frame for each probe - condition 
 combination ( averaged over 1000 frames ) .
border 
 color and style correspond to the probes : alexa 555 ( solid ) and r6 g 
 ( dashed ) and conditions : ph 3.5 ( cyan ) , ph 5.7 ( blue ) , and ph 8.7 
 ( red ) .
two distinct types of trajectory 
 profiles , seen in figure 2 , indicate the presence 
 of at least two modes of 
 interaction between the probes and film , depending on the solution 
 ph and probe charge . for the conditions with the fewest number of 
 events per frame ( alexa in mb water and tris buffer figure 2b , c , and r6 g in mb water and hcl figure 2e ,
we either observe a molecule for 1 frame or less , or we observe the 
 same molecule over multiple frames at the same location within our 
 static localization error ( 40 nm ) .
however , for alexa in hcl 
 and r6 g in tris , there is an additional type of trajectory involving 
 adsorption of the molecule followed by the movement of the molecule 
 to an adjacent location .
these trajectories are indicative of hindered 
 diffusion that is slow enough for us to track with our integration 
 time .
as we will demonstrate with radius of gyration evolution analysis 
 and an examination of the single frame displacement distributions , 
 we are observing molecules undergoing intermittent surface diffusion , 
 or  hopping  from one location on the surface to another , 
 similar to the desorption mediated diffusion identified by the schwartz 
 group for molecules diffusing at a solid - liquid interface , and the hopping we previously identified in 
 polyelectrolyte brushes .
we do not find 
 repeat adsorption events at specific sites that would be characteristic 
 of  hot spots 
, which have been observed in inorganic 
 substrates such as silica due to defects .
because hopping behaviors are important for molecular transport 
 near and within the film , we will focus our efforts on the conditions 
 where trajectories show hopping behavior ( examples shown in figure 2a , g ) .
radius of gyration 
 evolution quantitatively distinguishes periods of 
 immobilization vs diffusion within a trajectory , and was used to further 
 analyze the diffusive trajectories .
the radius of gyration of a particle ( rg ) is calculated at each point in the trajectory using 
 the following equation:2where r1 and r2 correspond to the major and minor eigenvalues 
 of the radius of gyration tensor t. the tensor corresponds 
 to the 2 by 2 matrix:3where n is the number of 
 steps in the trajectory , x and y are the x and y locations of the 
 particle .
the evolution of the radius of gyration with time is established 
 by calculating rg for each time step in 
 a trajectory .
figure 3a shows 
 the radius of gyration evolution of simulated brownian trajectories 
 generated with a 2d off lattice monte carlo random walk model and 
 simulated trajectories with periods of adsorption .
displacements were 
 drawn from normal distributions with widths corresponding to d = 0.01 m / s for the brownian trajectories , 
 and dunconfined = 0.1 m / s and dconfined = 0.0001 m / s for the trajectories with periods of confinement .
diffusors 
 had a 40% chance of becoming immobilized and once immobilized had 
 a 10% chance of becoming mobile again .
the radius of gyration evolution plots of 
 the brownian trajectories differ substantially from those of trajectories 
 with periods of adsorption . for brownian trajectories ,
conversely , the 
 slope of the radius of gyration evolution for trajectories with adsorption 
 is not constant .
when the probe jumps to a new location , there is a large increase 
 in slope .
small negative slopes in the radius of gyration are observed 
 after large displacements because the radius of gyration is effectively 
 a running average with a 1/n dependency .
( a ) shows radius of gyration 
 evolution curves for simulated brownian motion with d = 0.01 m / s ( blue ) and diffusion with confinement 
 with d = 0.1 m / s and dconf = 0.0001 m / s ( black ) .
( b ) five 
 trajectories of alexa 555 in acid over a 10 bilayer paa / pah film . 

the inset is a plot of the instantaneous slope of the yellow - green 
 curve in panel b with a red line drawn at the threshold used to determine 
 whether or not the molecule was stationary at each step .
( c ) five 
 trajectories of r6 g in tris buffer over a 10 bilayer paa / pah film .
evaluation of radius of gyration 
 evolution for experimental trajectories 
 demonstrates that the same molecule can switch between periods of 
 adsorption and hopping .
radius of gyration versus time plots for five 
 trajectories each of alexa 555 in hcl ( ph = 3.5 ) and r6 g in tris buffer 
 ( ph = 8.7 ) are shown in figure 3b , c . like the 
 radius of gyration evolution plots for the simulated trajectories 
 with adsorption
, these trajectories show distinct regions of adsorption 
 and hopping to a new area . in order to estimate how often particles 
 are adsorbed ,
a threshold is set equal to 0 plus 1.5 times the standard 
 deviation of the instantaneous slope of all trajectories .
the instantaneous 
 slope of the yellow - green line in figure 3b 
 and the threshold are plotted in the inset of figure 3 .
using this rough estimation , we find that on average , alexa 
 555 molecules in hcl spend more than 82% of their tracking time adsorbed , 
 while r6 g molecules in tris buffer spend more than 91% of their tracking 
 time adsorbed .
while the radius of gyration analysis works well for 
 our short trajectories , it should be noted that such analysis is not 
 appropriate for longer trajectories as switching behavior becomes 
 more difficult to detect near the end of long trajectories .
methods 
 such as sliding time window mean squared displacement methods would 
 be more appropriate for long trajectories .
analysis of the single frame 
 displacements is an effective method to quantify different mechanistic 
 dynamics .
the single frame displacement 
 is simply the distance that a tracked molecule moves from one frame 
 to the next .
this analysis can also provide the average diffusion 
 constants of the different transport modes .
we analyze the single 
 frame displacement data by generating histograms using all displacement 
 events in a given sample .
the mean and relative population of the 
 distributions is determined by using a markov chain monte carlo ( mcmc ) 
 algorithm to generate model distributions that are as close as possible 
 to the experimental data ( see the si for 
 the algorithm used ) .
the mcmc algorithm can be compared to fitting 
 the histograms ; however , it equally evaluates every data point and 
 is independent of the bin size .
an analysis of the single frame displacements 
 of the two probe molecules alexa 555 and r6 g under the three different 
 ph conditions confirms the presence of two modes .
figure 4 shows histograms of the single frame displacement 
 ( black dots ) along with a model distribution calculated using the 
 mcmc algorithm ( gray dots ) .
the distribution of the displacements 
 in log scale demonstrates that there are two populations : one representing 
 adsorbed particles characterized by short displacement steps indistinguishable 
 from the localization uncertainty , and one representing long displacement 
 steps attributed to hopping or confined diffusion .
the short 
 displacements are on average 40 nm , and represent immobile 
 molecules .
we do not expect adsorbed probe molecules to appear completely 
 stationary due to the localization uncertainty of our radial symmetry 
 fitting algorithm , which can vary due to experimental parameters such 
 as microscope focus .
there are also long displacements of more than 
 an order of magnitude greater than the adsorbed displacements which 
 are characteristic of mobile or hopping molecules .
three of the six 
 probe - ph combinations exhibit these hopping displacements : alexa in 
 hcl ( figure 4a ) , r6 g in tris ( figure 4f ) , and a small population of r6 g in hcl ( figure 4b ) .
there is also a small population of hopping 
 molecules for r6 g in water ( figure 4d ) , but 
 the contribution to the overall distribution is so small that the 
 center of the second distribution can not be calculated properly .
the 
 good agreement between the experimental data and the simulated mcmc 
 data confirms that our analytical results are consistent with two 
 coexisting modes of transport at the film water interface .
the 
 relative populations of the immobilized and hopping distributions 
 indicate that r6 g is immobilized 20% more frequently than alexa . for 
 alexa in hcl
the probability of an event belonging to the adsorbed 
 distribution is 55% , while the probability that it belongs to the 
 hopping distribution is 45% . for r6 g in hcl , the probabilities are 
 69% and 31% for the adsorbed and hopping distributions respectively , 
 and for r6
g in tris those probabilities are 79% and 21% . clearly , 
 based on these distributions ,
r6 g is less likely to hop from one site 
 to another regardless of the ph of the solution .
we expect uncompensated 
 pah in the outermost layer of the film to provide adsorption sites 
 for oppositely charged alexa 555 molecules .
if these sites are close 
 together , then the alexa molecules can easily hop between them .
uncompensated 
 paa would provide appropriate adsorption sites for r6 g , but paa is 
 not the outermost layer of the multilayer ; therefore , we expect r6 g 
 to have limited access to these sites , which may explain why we see 
 a lower probability of hopping for r6 g .
single frame displacement 
 histograms and diffusion coefficient 
 histograms for each probe at the three different ph conditions .
( a , c , e ) 
 single frame displacement histograms ( black ) and mcmc approximation 
 of the distribution ( gray ) for alexa 555 in hcl , mb water , and tris 
 buffer , respectively .
( b , d , f ) single frame displacement histograms 
 ( black ) and mcmc approximation of the distribution ( gray ) for r6 g 
 in hcl , mb water , and tris buffer , respectively .
parameters extracted 
 from the distribution , assuming log - normal distributions , are also 
 indicated , including the mean displacement for each distribution as 
 well as the probability of a displacement belonging to a distribution 
 ( if applicable ) .
( g , h ) distributions of the diffusion coefficient 
 calculated from each individual trajectory ( black ) and mcmc approximation 
 of the distribution using the shown parameters ( gray ) for alexa 555 
 in hcl and r6 g in tris buffer , respectively .
parameters shown are 
 the average d for each distribution and the probability 
 of a trajectory having a d that falls into that distribution . 

border color and style correspond to the probes : alexa 555 ( solid ) , 
 and r6 g ( dashed ) and conditions : ph 3.5 ( cyan ) , ph 5.7 ( blue ) , and 
 ph 8.7 ( red ) .
the distributions of 
 the diffusion coefficients ( figure 4g , h ) also 
 show two clear populations , further evidence 
 of two dynamic processes .
the diffusion coefficient summarizes the 
 average displacement of each single molecule over its observation 
 period , and is calculated by averaging the squared displacements of 
 each step in the trajectory .
the slower 
 diffusion distribution is centered at 7  10 nm / s for both the alexa and r6 g probes , and corresponds 
 to molecules that are adsorbed in the film .
the faster diffusion coefficient 
 is 720  30  10 nm / s for alexa 
 555 in hcl , while for r6 g in tris , it is somewhat slower , 220  
 20  10 nm / s .
these diffusion coefficients 
 are 12 orders of magnitude slower than previous measurements 
 of small molecules diffusing in pem films , where the lateral diffusion 
 coefficients of single neutral probes are on the order of 10 nm / s
. the slower diffusion 
 that we measured could be due to the fact that our probes are charged , 
 unlike the neutral probes used in the previous study , the result of a different polymer system , or molecules 
 that remain immobilized for the entire observation period .
a molecule is more likely to have a diffusion coefficient 
 that belongs to the faster diffusion distribution : 76% for alexa in 
 hcl , and 61% for r6 g in tris .
while this may seem to contradict our 
 previous conclusions that molecules are most likely to get stuck , 
 it is not surprising because the diffusion coefficient is determined 
 from the mean squared displacement of a trajectory that is calculated 
 from all of the single frame displacement events for each particular 
 molecule .
scatter plots of d vs trajectory length 
 ( figure s5 ) show that some of the shortest 
 trajectories ( less than 10 frames ) produce the fastest diffusion coefficients . 

these are likely trajectories in which the molecules are hopping for 
 the duration of the trajectory and escape the tirf excitation volume 
 before they become immobilized in the film .
thus , at least two types 
 of trajectories contribute to the distributions of d : short trajectories where the molecules are continuously hopping , 
 and longer trajectories that contain periods of immobilization .
photophysics due to blinking or bleaching is not a major contributor 
 to our ability to characterize the relative difference between adsorbed 
 and hopping displacements .
the experiments were repeated with the 
 laser power set to 5 , 10 , and 15 mw ( corresponding to 1.67 , 3.33 , 
 and 5 mw / cm ) in order to ensure that our measurements 
 were not significantly perturbed by photophysics . in the case of both 
 alexa in hcl and r6 g in tris ,
the average single frame displacement 
 for the adsorbed and hopping distribution does not change as the power 
 increases ( data not shown ) , and the percent of single frame displacements 
 belonging to the adsorbed distribution decreased by 5% after 
 the power was increased by 200% ( figure 5 ) . 
 despite this small increase ,
the overall difference in the relative 
 population of the adsorbed distributions of alexa 555 and r6 g remains 
 22% , suggesting that the higher probability of r6 g to become adsorbed 
 is not an artifact of photophysics .
the 
 explanation for the probe and condition mediated dynamics is likely 
 a combination of hydrophobic interactions along with electrostatics 
 and a change in film density , which are reversibly tuned by the ph 
 of the solution .
such a shift in ph causes changes to the relative 
 degree of polyelectrolyte ionization as discussed previously .
farhat 
 et al . found that the transport of ions through a pem was an electrostatic 
 process governed by hopping of the ions from one charged site in the 
 pem to another .
we used this work as 
 the basis to develop an electrostatic based mechanism for the tunable 
 surface interactions we measure .
because hydrophobic interactions 
 are also important for interfacial transport , we probed the contribution 
 of hydrophobic interactions by measuring the diffusion of rhodamine 
 b , a molecule with no net charge in water , over the pem .
we find that 
 the degree of association characterized by the number of events per 
 frame is similar to that of the charged probes in water , but the single 
 frame displacement distribution is drastically different with two 
 clear distributions instead of one , strongly supporting the notion 
 that electrostatic interactions are the primary determinant for how 
 molecules interact with the film .
percent single frame displacements belonging to the adsorbed 
 distribution 
 as a function of laser power for r6 g in tris buffer and alexa 555 
 in hcl .
the error bars are based on the standard deviation of the 
 sampling values of p ( the probability of adsorption ) 
 that we have defined in the si . for r6 g in hcl , both
the ionization of the probe 
 and outer film 
 layer promote repulsion of the probe molecules .
as the ph is increased , 
 the probe molecules become less ionized , as does the film to a much 
 lesser degree , allowing for the increased interaction of r6 g with 
 the film that we measure . for alexa 555 in hcl ,
the near complete 
 ionization of the probe and film create an electrostatic environment 
 that supports interaction , which is what we observe .
this electrostatic 
 attraction also explains the hopping behavior , as probe molecules 
 are more likely to interact with the film repeatedly after diffusing 
 away .
however , as the ph is increased , there is drastically decreased 
 interaction of the probe with the film , even though we expect both 
 to remain mostly ionized .
this observation is not intuitive and difficult 
 to explain , but could be due to a complex interplay of electrostatic 
 effects combined with steric and hydrophobic effects . for instance , 
 yip and lee found that coulombic repulsion had a negligible effect 
 on the loading of cationic r6 g molecules in a cationic polymer film , 
 while significant loading enhancement was found when using a negatively 
 charged dye in the same film .
they conclude that coulombic attraction 
 can play a significantly larger role on the incorporation of molecules 
 into a pem than coulombic repulsion , illustrating 
 that the electrostatic interactions of molecules in pems are complicated 
 and still not well understood .
it is possible that structural 
 properties of the film , such as 
 film density , reflecting the spatial configuration of the polymer 
 chains , contribute to the degree of association of the probes with 
 the film .
according to the estimates for the degree of ionization 
 discussed above , there should be a change in film structure upon the 
 change in ph from 3.5 to 8.7 . at a ph of 3.5
there is a difference 
 in the degree of ionization of pah ( nearly fully ionized ) and paa 
 ( 87% ionized ) .
this suggests that the structure of the film under 
 these conditions will be less compact than at higher ph values due 
 to less intrinsic charge compensation .
such a film is expected be 
 thick , with loops forming in the polymer chains resulting in a film 
 that is less compact .
this could explain why both probes appear to interact with the film 
 under acidic conditions , although r6 g interaction is not very favorable , 
 suggesting that the dynamics are not purely sterically mediated .
it 
 has been found that films constructed of polyelectrolytes that are 
 nearly fully ionized are thinner and contain more ordered polymer 
 networks .
it is therefore reasonable 
 to assume that contraction of the film will occur as ph is decreased , 
 resulting in a comparatively more dense film , which could explain 
 the apparent exclusion of both probes in water . upon increasing the 
 ph to 8.7 ,
the pah becomes less ionized , which could result in a swelling 
 of the film similar to that in a solution of ph 3.5 .
this swelling 
 combined with a decrease in ionization of the cationic pah and increase 
 in ionization of the anionic paa may create an environment less hostile 
 to r6g - film interaction .
we demonstrate ph - dependent 
 hopping of charged probe molecules 
 within a paa / pah pem in addition to reversible adsorption of probe 
 molecules .
these two transport modes exist for alexa 555 at ph 3.5 
 and r6 g at ph 8.7 but not for alexa at ph 8.7 or r6 g at ph 3.5 or 
 either probe in mb water ( ph 5.7 ) , with only adsorption present for 
 the other probe - condition pairs studied , resulting in tunable behavior 
 based on probe charge and solution ph
. radius of gyration evolution 
 analysis shows that for alexa in hcl and r6 g in tris , the transport 
 at the surface is governed by intermittent adsorption events .
cationic 
 r6 g is less likely to hop from one location to another under all conditions 
 compared to anionic alexa 555 , and we confirm that the tendency of 
 r6 g to remain adsorbed is not related to photophysics .
we propose 
 an electrostatic - based interaction mechanism to explain our results . 
 at low ph ,
excess positive charge in the outer layers of the film 
 promotes interaction with the anionic probe , while the cationic probe 
 is largely excluded . at high ph ,
the cationic sites in the outer layer 
 are sparser , resulting in decreased interaction of the anionic probes . 

the reversible transport tuning we demonstrate moves us one step closer 
 to the creation of optimal functionalized surfaces for specialized 
 applications in water filtration and remediation , drug loading and 
 release , and ion exchange separations .
 the 
 tunable nature of weak polyelectrolyte multilayers makes them 
 ideal candidates for drug loading and delivery , water filtration , 
 and separations , yet the lateral transport of charged molecules in 
 these systems remains largely unexplored at the single molecule level . 
 
 we report the direct measurement of the charge - dependent , ph - tunable , 
 multimodal interaction of single charged molecules with a weak polyelectrolyte 
 multilayer thin film , a 10 bilayer film of poly(acrylic acid ) and 
 poly(allylamine hydrochloride ) paa / pah . using fluorescence microscopy 
 and single - molecule tracking , two modes of interaction 
 were detected : 
 ( 1 ) adsorption , characterized by the molecule remaining immobilized 
 in a subresolution region and ( 2 ) diffusion trajectories characteristic 
 of hopping ( d  109 cm2/s ) . 
 radius of gyration evolution analysis and comparison 
 with simulated trajectories confirmed the coexistence of the two transport 
 modes in the same single molecule trajectories . 
 a mechanistic explanation 
 for the probe and condition mediated dynamics is proposed based on 
 a combination of electrostatics and a reversible , ph - induced alteration 
 of the nanoscopic structure of the film . 
 our results are in good agreement 
 with ensemble studies conducted on similar films , confirm a previously - unobserved 
 hopping mechanism for charged molecules in polyelectrolyte multilayers , 
 and demonstrate that single molecule spectroscopy can offer mechanistic 
 insight into the role of electrostatics and nanoscale tunability of 
 transport in weak polyelectrolyte multilayers . 
Introduction
Materials
and Methods
Results and Discussion
Conclusions