nanocontainers that 
 can bind and hold hydrophobic molecules have 
 attracted significant interest due to implications in areas such as 
 self - healing materials and drug delivery . among the factors 
 that are taken into account while arriving at a molecular design for 
 these containers , encapsulation stability is often considered a critical 
 one . encapsulation itself is often defined by 
 the loading capacity of the host , i.e. , the amount of guest molecule 
 that a host assembly can hold . this capacity is dictated by the thermodynamic 
 distribution coefficient of the guest molecule between the host and 
 the solvent . a feature that has not received much attention involves 
 the guest - exchange dynamics . this is important , as this is a direct 
 and arguably the most rigorous indicator of encapsulation stability 
 of a host assembly . considering the diversity 
 of the environments that a supramolecular assembly encounters in a 
 typical biological system , it is important that we understand the 
 influence of these external environmental factors upon encapsulation 
 stability . in this paper , we show that the mechanism of guest - exchange 
 dynamics and thus the factors that affect encapsulation stability 
 can greatly vary with environmental changes . three limiting 
 scenarios exist for the mechanism of guest exchange : 
 ( i ) collision  exchange  separation mechanism , ( ii ) exit  re - entry 
 mechanism , and ( iii ) fission  recombination mechanism . the first mechanism is collision - based , where the guest exchange 
 occurs only because of a collision between two host assemblies . the second pathway is diffusion - based , where the guest - exchange rate 
 depends on the ability of guest to exit and enter from the host assemblies . the third mechanism involves fragmentation of the host assembly into 
 two smaller entities as the first step , followed by a recombination 
 to regain the original host assembly ( figure s1 , supporting information ) . to simplify the possibilities , we 
 chose to use host assemblies that are based on cross - linked polymer 
 nanogels , which do not lend themselves to the third possibility . the 
 cross - linking feature of nanogels obviates the fission possibility , 
 and the two 
 viable pathways for the host assembly are illustrated in figure 1 . between these pathways , although the kinetic orders 
 of these mechanisms are different , it is difficult to quantify the 
 order of a molecular exchange process , as this is not a chemical reaction . 
 here , we design a series of experiments to probe the possible pathways 
 for guest exchange in these polymeric nanogels . schematic representation 
 of two possible mechanisms for guest exchange 
 between cross - linked nanogels : ( a ) the collision  exchange  separation 
 mechanism , also called the collision - based mechanism , and ( b ) the 
 exit  re - entry mechanism , also called the diffusion - based mechanism . we use the recently reported fluorescence 
 resonance energy transfer 
 ( fret ) as the tool to interrogate the guest - exchange process , which has proved to be quite a robust method 
 for a variety of host  guest assemblies . briefly , a hydrophobic fret pair , 3,3-dioctadecyloxacarbocyamine 
 perchlorate ( donor ) and 1,1-dioctadecyl-3,3,3,3-tetramethylindocarbocyanine 
 perchlorate ( acceptor ) , were independently encapsulated in otherwise 
 similar nanogel hosts . when these solutions were mixed , the emission 
 spectrum of the mixed solution in response to donor excitation at 
 450 nm was monitored over time . no fret would be observed if the two 
 dye molecules are stably encapsulated and continue to be in their 
 separate nanocontainers , since the distance between the two dye molecules 
 is much higher than their frster radii . on the other hand , 
 if the guest exchange between the host and its surroundings was significant , 
 the extent of fret would evolve , as the guest composition in the nanogel 
 changes over time . 2,2-dithiodipyridine , 2-mercaptoethanol , 
 poly(ethylene glycol ) monomethyl ether methacrylate ( pegma , mw 450 ) , 2-(diisopropylamino)ethyl methacrylate 
 ( dpa ) , d , l - dithiothreitol ( dtt ) , 1,1-dioctadecyl-3,3,3,3-tetramethylindocarbocyanine 
 perchlorate ( dii ) , 3,3-dioctadecyloxacarbocyanine perchlorate 
 ( dio ) , 4-cyano-4-(phenylcarbonothioylthio)pentanoic acid , and other 
 conventional reagents were obtained from commercial sources and were 
 used as received without further purification . pyridyl disulfide 
 ethyl methacrylate ( pdsema ) was prepared using a previously reported 
 procedure . the ph value was determined 
 via the accumet ab 15/15 + benchtop ph meter . h nmr spectra 
 were recorded on a 400 mhz bruker nmr spectrometer using the residual 
 proton resonance of the solvent as the internal standard . molecular weights 
 of the polymers were estimated by gel permeation chromatography ( gpc ) 
 using pmma standard with a refractive index detector . dynamic light 
 scattering ( dls ) measurements were performed using a malvern nanozetasizer . uv  visible absorption spectra were recorded on a varian ( model 
 el 01125047 ) spectrophotometer . transmission electron microscopy 
 ( tem ) images were taken using a jeol 2000fx at 200 kv . random copolymer p2 , containing dpa groups , was synthesized according to a 
 previously reported procedure . a mixture 
 of 4-cyano-4-(phenylcarbonothioylthio)pentanoic acid ( 12.0 mg , 0.043 
 mmol ) , pdsma ( 150.0 mg , 0.588 mmol ) , pegma ( 215.0 mg , 0.453 mmol ) , 
 dpama ( 130.0 mg , 0.609 mmol ) , and aibn ( 1.5 mg , 0.010 mmol ) was dissolved 
 in thf ( 1.0 ml ) and degassed by performing three freeze  pump  thaw 
 cycles . the reaction mixture was sealed and then transferred into 
 a preheated oil bath at 65 c and stirred for 10 h. to remove 
 unreacted monomers , the resultant mixture was precipitated in cold 
 diethyl ether ( 20 ml ) and redispersed in thf three times to yield 
 the random copolymer p2 as a waxy solid . h nmr ( 400 mhz , cdcl3 )  : 8.46 , 7.67 , 7.10 , 
 4.354.09 , 3.943.37 , 3.02 , 2.62 , 2.041.64 , 
 1.430.87 . the molar ratio ( pds / peg / dpa ) was determined to 
 be 34%/28%/38% by integrating the methoxy protons in the polyethylene 
 glycol unit ( hd = 3.37 ppm ) , the aromatic protons 
 in the pyridine ( ha = 8.46 , hb = 7.67 , hc = 7.10 ) , and the methylene protons 
 next to the nitrogen in dpa units ( he = 2.62 , hf = 3.02 ) . polymer ( 10 
 mg ) was dissolved in 1 ml of water , and the ph was adjusted to around 
 10 through the addition of naoh aqueous solution ( 1 m ) . then 0.04 
 ml of dii in acetone stock solution ( 5 mg / ml ) or 0.08 ml of dio in 
 acetone stock solution ( 2.5 mg / ml ) was added into the polymer solution 
 ( 0.2 mg of each dye for 10 mg of polymer in 1 ml of water ) . the mixed solution was stirred 
 overnight at room temperature , open to the atmosphere to allow the 
 organic solvent to evaporate . then a measured amount of dtt ( 0.2 mol 
 for 15 mol % against pds groups ) was added . after stirring for 4 h , 
 insoluble dii / dio was removed by filtration and the pyridothione byproduct 
 was removed from the nanogel solution by extensive dialysis using 
 a membrane with a molecular weight cutoff of 7000 g / mol . finally , nanogel stock solutions with a concentration of 1 mg / ml were prepared 
 for further studies . nanogel containing 
 dii and nanogel containing dio were mixed in phosphate buffer solution 
 at ambient temperature and at a certain ph value such that the total 
 volume was 1 ml . at the 
 same time , absorption spectra were also measured for all samples to 
 ensure that there is no loss of dye molecules due to precipitation . the fret ratio ia/(ia + i d ) , where ia and i d are the fluorescence 
 intensities of the acceptor ( dii ) and the donor ( dio ) , respectively , 
 was plotted against time to show the dynamics of the dye exchange 
 in nanogel solution . the leakage coefficients (  ) were calculated 
 on the basis of the slopes from four earlier points in the linear 
 regime . in the case of very fast guest exchange , two cross - linked polymeric nanogels were used in this study . the 
 first nanogel ( ng - c ) is based on a random copolymer ( p1 ) , formed from a hydrophilic oligoethylene glycol ( oeg ) 
 functionalized methacrylate monomer and a hydrophobic pyridyl disulfide 
 ( pds ) functionalized methacrylate monomer ( scheme 1 ) . the second nanogel ( ng ) and its precursor 
 ( p2 ) contain a diisopropylamine ( dpa ) functionalized 
 methacrylate as a comonomer in addition to the oeg- and the pds - functionalized 
 monomers . the size of these two types 
 of nanogels at neutral ph was found to be very similar ( figure 2 ) . size distribution of nanogel at different ph values via dls measurements : 
 ( a ) ng with 30% cross - linking density and ( b ) ng - c with 20% cross - linking density . first , we were interested in understanding the mechanism 
 of guest 
 exchange in the control nanogel ng - c , which is not sensitive 
 to the external environment , as this provides the baseline for our 
 study . among the collision- and diffusion - based pathways , one would expect strong and positive correlations between the collision 
 frequency and the concentration of nanogels in solution . we used the 
 fret - based method , which provided a measure of the dye exchange rate 
 in the form of the leakage coefficient (  ) , which can be obtained 
 as the initial slope of the linear fit ( earlier four points in the 
 linear regime ) by plotting the fret ratio ia/(ia + i d ) against time , where ia and i d are the fluorescence intensities of the acceptor 
 ( dii ) and the donor ( dio ) respectively . the concentrations of the 
 nanogels were varied as 0.05 , 0.10 , and 0.15 mg / ml for both ng - c containing dii and ng - c containing dio at 
 ph 7.1 . figure 3c shows that there was indeed 
 a faster evolution of fret with time in the nanogels with a concentration 
 of 0.15 mg / ml , compared to those with a concentration of 0.05 mg / ml 
 ( figure 3a ) and 0.10 mg / ml ( figure 3b ) . values of 0.0192 , 0.0284 , and 0.0315 
 min were observed for the concentrations of 0.05 , 
 0.1 , and 0.15 mg / ml , respectively , indicating that the guest exchange 
 between nanogels indeed increased with increasing concentration ( figure 3d ) . these data provide the initial evidence that 
 the guest exchange in these control nanogels happens via the collision - based 
 mechanism as the dominant pathway . fluorescence evolution when ng - c respectively containing 
 dii and dio are mixed in solutions at ph 7.1 : ( a ) 0.05 mg / ml , ( b ) 
 0.10 mg / ml , and ( c ) 0.15 mg / ml . ( d ) comparison of the dynamics of 
 guest exchange between ng - c with different concentrations 
 at ph 7.1 . additionally , the size of the 
 nanogel would also impact guest exchange , 
 if the collision - based mechanism was the dominant mechanism for guest 
 exchange , since the collision frequency would be affected by the size 
 of nanogels . the ph - sensitive nature of the dpa moieties endows ng with ph - dependent size variations in this nanogel . the 
 size of ng increases with decreasing ph , while the size 
 of ng - c does not change with ph ( figure 2 ) . figure 2a shows that the sizes of ng increased from 10 to 18 nm when the ph changed from 8.0 
 to 5.1 . the observed size increase in ng is attributed 
 to the protonation of the dpa units , which presumably results in the 
 swelling of the nanogels due to electrostatic repulsion between these 
 positively charged dpa groups inside . as the size of ng varies with ph , we expected that the dye - exchange rate would also 
 change with the ph . figure 4a shows that 
 there is a rapid evolution 
 of fret with time for ng at ph 8.0 . on the other hand , ng at ph 6.4 exhibits little change in fret ratio with time 
 and thus , the exchange rate indeed decreased from a  value 
 of 0.080 min at ph 8.0 to 0.004 min at ph 6.4 ( figure 4d ) . these results are 
 consistent with the collision - based mechanism , as the size of ng indeed affected the rate of guest exchange , providing further 
 evidence that the dominant guest exchange in nanogels might happen 
 via the collision - based mechanism . it should be noted , however , that 
 while the collision frequency is expected to decrease with increase 
 in size , because of the slower diffusion ( via the stokes  einstein 
 equlation ) , it is also known that the collision frequency can increase 
 with an increase in size . one possible 
 explanation is that the number of effective collisions , i.e. , collisions 
 that result in guest exchange , decrease with an increase in size . this is reasonable , as the effect of the reduced diffusion could potentially 
 reduce the effective collisions . this explanation is consistent with 
 the results but remains provisional , as there are no established quantitative 
 relationships to this effect at this point . fluorescence evolution 
 when two ng solutions independently 
 containing dii and dio dye molecule as guest are mixed in solutions 
 at different ph values : ( a ) ph 8.0 , ( b ) ph 6.4 , and ( c ) ph 5.1 . ( d ) 
 guest - exchange rates between ng at different ph values . the concentration of each nanogel was 0.10 mg / ml . interestingly , however , an unexpected change in the fret 
 evolution 
 occurs below ph 6.4 , even though the size - increase is observed through 
 the entire ph range from 8.0 to 5.1 . from ph 6.4 to 5.1 , the fret 
 evolution was found to increase ( figure 4c ) . figure 4d shows that the exchange rate systematically 
 increases with decreasing ph from 6.4 to 5.1 . the  value of 
 0.004 min at ph 6.4 increased back to 0.083 min at ph 5.1 . since the size of the nanogel increases 
 with decreasing ph , including at this ph range , these results are 
 not consistent with the collision - based mechanism therefore , it is 
 possible that the diffusion - based pathway is the dominant operating 
 mechanism in this scenario , providing the first indication that there 
 might be an environment - dependent change in mechanism . however , a 
 few alternating possibilities need to be considered prior to reaching 
 this conclusion . first , it is possible that the dye molecules 
 themselves have a 
 certain ph - dependent solubility and thus is affecting the guest molecule 
 exchange in the collision state . to test this possibility , we investigated 
 the ph - dependence of guest - exchange dynamics in ng - c , 
 where the size of the nanogel does not change with ph . figure 5a , b shows that there was indeed similar evolution 
 of fret with time in the nanogels at ph 8.0 and 7.1 , while a slightly 
 faster fret evolution was observed at ph 6.1 ( figure 5 ) . we attribute the small ph - dependence to the possibility 
 that the solubility of dii and dio molecules may vary at different 
 ph values . the solubility may be improved a bit at low ph due to the 
 presence of tertiary amine ( scheme 1 ) , leading 
 to easier dye exchange during the collision . note that we do not observe 
 any significant dye loss in the nanogel during our fret experiments , 
 which suggests that the repulsion between these positively charged 
 dyes and protonated ng at lower ph might be very small . two features are noteworthy in these results : first , the magnitude 
 of difference in exchange dynamics is too small compared to those 
 observed with ng and , therefore , does not account for 
 the results observed with ng . second , the guest - exchange 
 kinetics continues to increase with ph and there is no change in the 
 trend after ph 6.4 . these results suggest that the results observed 
 in ng are not due to the inherent difference in dye molecule 
 behavior at different ph values . comparison of the dynamics of guest exchange 
 between ng - c with 0.10 mg / ml at different ph values . we hypothesized next that the 
 observed change in ph - dependence 
 trend at ph 6.4 could perhaps be explained by a change in the hydrophobicity 
 of the nanogel interior , i.e. , the host properties . it is reasonable 
 to anticipate that the protonation of dpa groups would decrease the 
 hydrophobicity of the nanogel . specifically , the ratio of the intensities between the first and 
 the third peaks ( i1/i3 ) in the pyrene emission spectrum can be used to determine 
 the polarity of the dye s microenvironment . the value of this 
 ratio can range from 1.9 in polar solvents to 0.6 in certain hydrocarbon 
 solvents . we utilized this dye as the guest molecule to probe the 
 hydrophobicity of the microenvironment within the nanogel interiors . aqueous buffer solutions of ng containing 2 wt % pyrene 
 were prepared for this purpose at different ph values . the hydrophobicity of nanogel at different ph values was studied by 
 calculating the intensity ratio of the first and third emission peaks 
 of pyrene , commonly referred to as the i1/i3 ratio . figure 6b shows the variations in i1/i3 of pyrene encapsulated in ng at 
 different ph values . when the ph was reduced from 8.0 to about 6.4 , 
 the i1/i3 remained 
 constant around 1.25 . however , when the ph was further decreased , 
 a steady increase in the i1/i3 value was observed , suggesting that the microenvironment 
 of the dye is becoming increasingly polar . the i1/i3 ratio at ph 5.1 was found 
 to be about 1.37 . on the contrary , pyrene in the control nanogel ng - c ( that lacks the dpa units ) did not exhibit any discernible 
 change in the i1/i3 ratio over the same ph range of 5.18.0 , suggesting 
 that the hydrophobicity of these nanogels was not ph - dependent . ( a ) fluorescence emission spectrum 
 measured for nanogel ng - c loading 2 wt % pyrene and ( b ) 
 calculated i1/i3 ratios for nanogels at different ph values ( black , ng ; red , ng - c ) . while the environment inside ng was quite hydrophobic 
 between ph 8.1 and 6.4 , it became less hydrophobic when the ph value 
 decreased from 6.4 to 5.1 , which indicates that the ability of ng at these ph values to encapsulate the dii or dio molecules 
 could be greatly depleted . our studies with the control nanogel ng - c also suggest that the solubility of these dye molecules 
 can be slightly improved at lower ph . therefore , the dye might be 
 able to exit one nanogel and diffuse through the solvent to re - enter 
 another ; i.e. , the diffusion - based mechanism is possible in this case . thus , these results suggest that the guest exchange is primarily based 
 on the collision - based mechanism from ph 8.0 to 6.4 , but changes to 
 a diffusion - based mechanism below ph 6.4 . comparison of the dynamics 
 of guest exchange between ng of different concentrations 
 ( 0.05 , 0.10 , and 0.15 mg / ml ) at ( a ) 
 ph 8.0 , ( b ) ph 7.1 , ( c ) ph 6.1 , and ( d ) ph 5.1 . to further test this possibility , we investigated the effect 
 of 
 nanogel concentration on the guest - exchange rate at different ph values 
 in ng . we varied the concentrations of ng samples ( 0.05 , 0.1 , and 0.15 mg / ml ) and studied their fret evolution 
 at ph 5.1 , 6.1 , 7.1 , and 8.0 . figure 7a , b shows 
 that the exchange rates increase with nanogel concentration at both 
 ph 7.1 and 8.0 . this suggests that the guest exchange at these ph 
 values indeed occurred mostly via the collision - based mechanism . however , 
 while there is no clear trend at ph 6.1 ( figure 7c ) , the guest - exchange rate became slower with increasing concentration 
 at ph 5.1 , as  values of 0.098 , 0.083 , and 0.046 min were observed for nanogel concentrations of 0.05 , 0.1 , and 0.15 
 mg / ml , respectively ( figure 7d ) . note that 
 in a diffusion - based mechanism , the diffusion rate of dye out from 
 the nanogel should depend on the concentration of nanogels in solution . 
 at higher concentrations , the concentration of the host nanogel is 
 higher , while the concentration of the dye is very low at all these 
 concentrations . in this case , the driving force for the guest molecules 
 to diffuse into the solvent from the host nanogel is lower at higher 
 host concentrations . therefore , the observed decrease in guest - exchange 
 rate with the increasing nanogel concentration supports the assertion 
 that a diffusion - based mechanism is dominant at ph 5.1 . if our 
 hypotheses were correct , it should also follow that there 
 should not be any change in the mechanism of guest exchange in ng - c , as the hydrophobicity of its interior does not change 
 with ph . to perform this control experiment , we investigated the ph - dependent 
 trends at different concentrations of ng - c . the concentration 
 dependence of guest exchange was similar for this nanogel at all ph 
 values ( figure s6s8 , supporting information ) . indeed , the fret evolution increased with concentration at all 
 four ph values ( figure s9 , supporting information ) , indicating that the guest - exchange rate indeed increased with 
 the increasing concentration . this suggests that the operating mechanism 
 is collision - based and is not dependent on ph in the ph - insensitive 
 nanogel ng - c . the results from the control nanogel are 
 consistent with our conclusions for the ph - sensitive nanogels ng . in summary , we have designed a series of 
 experiments to study the 
 guest - exchange mechanism in ph - sensitive nanogels along with ph - insensitive 
 nanogels as a control . we have shown that the dominant mechanism for 
 guest exchange in these ph - insensitive nanogel hosts is collision - based . perhaps , the most important take - home message of this work is that 
 the mechanism of guest exchange in the ph - sensitive host  guest 
 assemblies can change on the basis of the microenvironment of the 
 host . when the nanogel interior is hydrophobic , the collision - based 
 mechanism is the dominant pathway . however , when the interior is sufficiently 
 hydrophilic , the dominant mechanism changes to a diffusion - based one . 
 from an even broader perspective , it is important to recognize that 
 both the intrinsic factors , such as size and interior environment 
 of the host assemblies , and the extrinsic factors , such as ph and 
 concentration , can have significant impact on encapsulation stability . 
 from the application standpoint , these findings could have implications 
 in many areas . for example , in drug delivery applications , the drug - loaded 
 nanocarrier experiences both concentration and environmental changes 
 upon biodistribution to diseased tissues . the mechanistic variations 
 in two different environments provide insights into molecular designs 
 that can afford stable encapsulation in one environment and release 
 of the molecules in another . similarly , the results 
 from this study may also provide new opportunities for designing nanoreactors in which catalysts encapsulated in a host can be used to reversibly 
 turn a chemical reaction on or off , because of the environment - dependent 
 diffusion of reactant molecules .