Temperature Driven Macromolecule Separation by Nanoconfinement

Article pubs.acs.org/Macromolecules

Temperature Driven Macromolecule Separation by Nanoconfinement Ilaria De Santo,†,§ Filippo Causa,‡,§ and Paolo A. Netti*,†,‡,§ †

IIT@CRIB, Centre for Advanced Biomaterials for Health Care, Istituto Italiano di Tecnologia, Largo Barsanti e Matteucci, 80125 Napoli, Italy ‡ CRIB, Centro di Ricerca Interdipartimentale sui Biomateriali, Università degli studi di Napoli Federico II, Piazzale Tecchio 80, 80125 Napoli, Italy § Dipartimento di Ingegneria Chimica dei Materiali e della Produzione Industriale, DICMAPI, Università degli studi di Napoli Federico II, Piazzale Tecchio 80, 80125, Napoli, Italy S Supporting Information *

ABSTRACT: We focused on the influence of temperature variations on macromolecule partitioning between unconfined and nanoconfined areas in nanoslits using single molecule measurements. We evaluated the number of fluorescent poly(ethylene glycol) (PEG) molecules confined in glass nanoslits in several configurations by fluorescence correlation spectroscopy (FCS) and recorded a decreasing trend in molecule partitioning within the confined environment when increasing the temperature. The trend is size-dependent, demonstrating the manipulation and size separation of a bimodal solution of uncharged macromolecules confined in nanochannels. These findings can have an impact on molecule manipulation and concentration, so far achieved mainly adopting external fields operating on charged molecules.

T

the free energy of confinement, which is the energy penalty due to the transfer of a molecule to a confined area with respect to the bulk. It is relevant to assess whether the thermodynamic equilibrium that is established in nanoslits (i.e., in a narrow pore) is affected by temperature changes. There is evidence of such dependence in the chromatography domain, since the interactive mode theory and its simulation analysis predict that temperature affects partitioning, and all the chromatographic modes result tunable by varying the temperature of the operating conditions.14 We considered that the free energy of confinement might also depend on temperature in certain conditions. In particular, standard theory predicts that K is temperature independent in the case of absence of surface interactions at fixed confining ratios,15 while it varies in the case of surface adsorption.16 Indeed, surface adsorptions have been recently noted for confined macromolecules in nanostructures.17−19 Although relevant to several phenomena, only a few studies at a molecular level focus on the confinement-mediated partitioning of macromolecules; an improvement in the comprehension of such mechanism could contribute to its downscaling in micro- and nanofluidic applications. In situ measurements of polystyrene partitioning between the nano-

he understanding of confinement-mediated passive partitioning of macromolecules within nanocavities was first of interest in the chromatographic context.1 Recently, it has gained greater attention since it can also support the development of biopolymer separation systems in nanoconfinement. Indeed, the improved capabilities of micro- and nanofabrication techniques and the advantage of small sample volume requirements2−4 have seen a recent boost in the development of macromoleculesmainly DNAseparating systems exploiting confinement effects, as in entropic traps, solid-state nanopores, nanoslits, nanochannels, and artificial sieving structures,5−8 or through exploitation of the Soret effect across thermal gradients.9,10 However, the understanding of the influence of temperature variations on confined macromolecules partitioning in nanostructures is still unsatisfactory also in equilibrium conditions. In addition, there is so far no experimental report on how temperature may affect partitioning. In passive conditions, the thermodynamics of confined polymers dictates the efficacy of a polymer separation process between a confined pore and the external solution through the partitioning coefficient K, which is the pore/channel to bulk concentration ratio at equilibrium K=

Cnano C bulk

(1)

Received: September 3, 2014 Revised: November 28, 2014 Published: December 10, 2014

where Cnano represents the concentration of nanoconfined molecules.11−13 K is related to the polymer concentration and © 2014 American Chemical Society

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Figure 1. (a) Cartoon of nanofluidics employed. (b) Cartoon of relevant dimensions in experiments. (c) Lateral beam waist size wxy temperature calibrations: confocal volume lateral dimension as a function of temperature measured in bulk (red spheres) and in glass nanochannels (black squares). (d) Radius of gyration for PEG20 (purple), PEG30 (green), and PEG40 kDa (blue) in water solution and persistence length of PEO41.5 kDa adapted from SANS experiments.25 Slopes of FCS and SANS data match within statistical error.

dependence of the properties of the material adopted for optical inspections (Nunc Lab-Tek or nanochannels). Recently, a different calibration method has been proposed for FCS measurements at different temperatures based on a double measurement in reference medium with the same refractive index.24 Though highly advantageous for analyses on a variety of samples and concentrations, this procedure is not necessary for the unique very diluted polymer concentration we used, which does not cause further refractive index variations. The polymer concentration considered here was 0.02% w/w, below the overlap polymer mass fraction in water solutions (0.5− 2%),25 to statistically observe single molecule properties during fluorescence fluctuations records, while the temperature range investigated, 23−45 °C, lies below the spinodal temperature estimated around 100 °C for the PEG/water LCST system.26 The radius of gyration rg is represented in Figure 1d, as it is more appropriate to describe the effective dimension of a confined polymer. The dimensions of rg were evaluated through polymer theory prediction rh = 0.665rg from measured hydrodynamic radii rh (see Experimental Procedures).27 The radius of gyration is found to slightly decrease as the temperature increases. In all cases rg values are above 5 nm (minimum value assumed 6.3 ± 0.2 nm), and the expected dependence of the molecule size on the polymerization grade is kept at all temperatures.28 Available small-angle neutron scattering (SANS) measurements for comparable diluted solutions of PEO41.5 kDa in water show the dependence of the polymer persistence length on temperature, which is analogous to the dependence of the rg on temperature measured by FCS.25 This result corroborates the calibration procedure adopted for the system investigated. The concentrations of confined PEG chains in 10 nm height borosilicate nanoslits for three MWs, 20, 30, and 40 kDa, each loaded independently in different nanoslits, were measured at three different temperatures: 23, 37, and 45 °C. Although entrance effects should not deeply affect the equilibration process as predicted by simulation results, measurements were carried out at the same distance from the nanochannel entrance, i.e., 50 μm from lateral micrometric reservoirs.16

pores of silica beads and their exterior were made to illustrate the principle of the high osmotic pressure chromatography technique,15,20 where only the size exclusion behavior is accounted for.11 Results at a static molecular level in a general scenario, where surface interactions might exist, are scarce for both monodisperse and polydisperse polymer mixtures, as well as for systems that account for variations in temperature. Here a molecular-level assessment of macromolecule partitioning in nanoslits upon temperature changes is obtained through fluorescence correlation spectroscopy (FCS) measurements.21,22 We show a temperature-driven separation mechanism for confined macromolecules, based on the controlled perturbation of the thermodynamic equilibrium of a confined macromolecule defined by two energetic contributions, the entropic penalty associated with confined configurations, and the enthalpy gain due to surface adsorption. The thermodynamic balance is affected by temperature variations in such a way that the confined configuration becomes more energetically unstable for larger molecules than it does for smaller ones when increasing the temperature. This behavior is demonstrated for PEG molecules by monitoring their concentration in confining 10 nm height borosilicate nanoslits at different temperatures (see cartoon of employed geometry in Figure 1a,b) with FCS.

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RESULTS Molecular dimensions for fluorescently labeled PEG20, PEG30, and PEG40 kDa were evaluated in water solution as a function of temperature from the diffusion time measured through the decorrelation time of the auto correlation functions (ACFs) of the fluorescence intensity traces recorded in the confocal volume by FCS (see Experimental Procedures). These measurements rely on a proper calibration of the confocal volume at different temperatures obtained from reference diffusivities of the common Rhodamine B (RB) dye at those temperatures. Indeed, the media refractive index changes with temperature causing the confocal volume to vary and, in particular, to increase.23 As shown in Figure 1c, the confocal volume, and in particular its lateral waist size wxy, expands in 8755

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Several ACFs were recorded at each temperature to gain statistics of the stochastic process, and the average curves are reported for PEG40 kDa in Figure 2 at each temperature.

Figure 3. Macromolecules concentration in the nanochannel measured at 23 °C (black symbols) and followed by time after the temperature shift to 37 °C (orange symbols), for both PEG20 (squares) and PEG40 kDa (circles) contemporarily loaded.

Figure 2. ACFs of PEG40 kDa confined in 10 nm channels at 23 (violet lines), 37 (black lines), and 45 °C (red lines). Averaged curves are reported as ticker lines. As temperature increases, the G(0) shifts to higher values. In the inset the powers of time dependence of the MSDs, α, evaluated for PEG20 (purple), PEG30 (green), and PEG40 kDa (blue) confined in 10 nm channels at 23, 37, and 45 °C.

gyration, which is higher for the larger PEG. On the other hand, the contribution of enthalpy to the thermodynamic balance of confined molecules is only a linear function of the molecular weight.12 The partitioning dependence on temperature was measured at several temperatures, namely 23, 32, 37, and 45 °C, allowing the attainment of equilibrium between temperature variations. Concentrations normalized to the concentration measured at 23 °C are reported as a function of temperature for both MWs in Figure 4a. By increasing the temperature, a decrease in the number of confined macromolecules according to molecular size was measured. In particular, PEG20 are still around 25% inside the confined space at 45 °C, while larger molecules are less than 0.07% of the initially loaded amount (see Supporting Information). Larger macromolecules get out of the nanochannel at a higher extent compared to smaller ones, and the ratio of KPEG20/KPEG40 increases by rising temperature. Noticeably, PEG20 kDa has a partitioning coefficient 10 times higher than PEG40 kDa at 45 °C, while being only twice larger at 23 °C (see Figure 4b). Indeed, it is predicted that a higher MW molecule is more excluded than a small molecular weight when the adsorption interaction energy is still unsatisfactory to balance the entropic penalty associated with a confined polymer configuration.16 In addition, an approximately linear relationship between the ratio of partitioning values and temperatures is seen in Figure 4b. Interestingly, the measured ratio KPEG20/KPEG40 changes in the case of monodisperse or bimodal mixtures. In fact, an increase of about 20% in the ratio KPEG20/KPEG40 in the case of bimodal mixture with respect to the monodisperse solutions was measured. Theoretical understanding of the thermodynamics of a bimodal mixture is still unsatisfactory and far from clarifying partitioning results, though it is predicted that the effect of the large molecular weight molecule is to increase the number of small molecules in comparison to its partitioning in monodisperse conditions.30 For the bimodal mixture, theory predicts the occurrence of the partitioning inversion (K of the low-MW component >1) in specific conditions and a strongly enhanced partitioning for the low-MW component, which is indeed aligned with our findings.15 In addition, by single molecule observations obtained through FCS, we monitored a change in the dynamics of molecules when contemporarily loaded. In Figure 5 we reported the ACFs for both PEG20 and PEG40 when loaded

There is a clear ascending trend in the G(0) values with temperature variations. Since the inverse of the ACF at zero τ corresponds to the molecule number in the illuminated volume,29 the number of confined molecules in the nanochannel decreases while increasing temperature. Similar trends in the ACFs were obtained for PEG20 and PEG30 kDa molecules (data not shown), again corresponding to a decrease in the number of confined molecules. The ACFs show a nonlinear dependence of the mean-square displacement (MSD) with time. The nonlinearity is represented by the power law coefficient α, which was already observed to decrease with the confinement extent, and to correlate with adsorption and desorption phenomena at the walls.17 α does not change with temperature for each MW staying around 0.6, as reported in the inset of Figure 2 (see Methods for fitting models for the ACFs). Alterations in the ACF at zero τ with increasing temperature were recorded also in nanochannels loaded with an equimolar dilute solution (1.3 μM each) of a bimodal mixture of two competitive MWs differently labeled, PEG20 and PEG40 kDa. Concentration in these conditions guarantees an average occupancy of the confocal volume of only one molecule, thus to discard interactions among different polymer chains. In Figure 3 we reported the nanochannel concentrations of both molecules at 23 °C and at different time points after the temperature setting of 37 ± 1 °C, as indicated by a thermocouple connected to the nanochannel external surface. The concentration in the nanochannel at a 50 μm distance from the reservoirs decreases and equilibrates in about 30 min for PEG20, while for PEG40 it equilibrates in a few minutes after the temperature is set. The measured time scale of this emptying process is of a few minutes. After such time the inner concentration equilibrates reaching a different partitioning value. The motivation for the different draining times for the two molecule sizes is probably related to a diverse entity of the driving force for this draining process, which could be possibly addressed to the difference in the entropic penalty associated with the temperature variation in the system. Indeed, the entropic penalty is a function of the square of the radius of 8756

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Figure 4. (a) Macromolecular concentration in nanochannel at different temperatures normalized to concentration at 23 °C for a bimodal mixture of PEG20 and PEG40 kDa. (b) Ratio in macromolecular partitioning of PEG20 and PEG40 kDa in nanochannels at different temperatures. The difference in partitioning is temperature sensitive. The high molecular weight molecule remains outside the nanochannel with a KPEG40 of lower than 0.1 as the temperature increases.

Figure 5. Average ACFs for contemporarily loaded PEG20 and PEG40 kDa at two indicative temperatures of 23 (circles) and 45 °C (squares). ACFs for PEG20 show substantial 2D diffusion behavior (red dash), while the ACFs of the high molecular weight molecule are not affected by the presence of the other compound and still show anomalous behavior (solid black line), which is interpreted as diffusion and adsorption−desorption phenomena at the walls (gray dot) (see eq 7).

to 16 ± 3 ms (bimodal). On the other hand, results of fitting of PEG20 ACF at 23 °C to eq 7 give a much faster desorption time of about 5 ± 2 ms in the bimodal solution compared to the larger value obtained in the monodisperse case (∼100 ms). PEG20 dwelling at the walls is much faster, being probably depleted from the surfaces by the larger molecules. In the bimodal solution, on the contrary, the dynamics of PEG40 is almost not affected by the presence of the small molecule. This is in agreement with the theory of adsorption of a bimodal mixture of competitive macromolecules, where the high molecular weight is predicted to replace the small compound on the surfaces which is let free in solution, since the entropy of mixing of the solution decreases in accordance with chain length.31 Interestingly, at higher temperatures, the PEG20 unbound fraction goes from 0.7 to 0.5 while the desorption time increases slightly. The opposite trend is found for the larger molecule. This could be addressed to the reduction in concentration of the PEG40 in the nanochannel and consequently to a relative increase of PEG20 at the walls (see Figure S4 in the Supporting Information).

in an equimolar bimodal mixture at two indicative temperatures of 23 and 45 °C. The ACF shape for the PEG20 in the presence of the other molecule at both temperatures can be almost interpreted with a 2D unconfined diffusion process, while the ACF of the high molecular weight molecule cannot be fitted to the same model, as shown by the red dashed lines in Figure 5. In particular, when forced to fit to eq 6 (solid lines in Figure 5), ACFs of PEG20 show an anomalous parameter of about 0.8 at both temperatures, compared to 0.6 found in the monodisperse solution (see inset of Figure 2). PEG40 ACFs do not show such variation from the monodisperse case; indeed, when fitted to eq 6, the fitting parameter α stays constant around 0.5. Thus, the contemporary loading of low and high MW molecules affects the diffusive behavior of the low molecular weight molecule, while the larger molecule is not affected by the presence of the other compound and still shows a profound anomalous behavior (at any temperature investigated). The same curves can also be interpreted with a twodimensional diffusion model that accounts for adsorption− desorption phenomena at the walls (see eq 7 in the section “FCS in Nanochannels” for details). For PEG40 the unbound state probability is around 0.7 at any temperature, for both the monodisperse and bimodal solution, and the desorption time shows a very slight decrease from 50 ± 20 ms (monodisperse)

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DISCUSSION There are several chemical physical parameters that affect the number of molecules residing in a nanochannel with respect to temperature changes. Indeed, the confined energetic config8757

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be negative, as are those representative of an exothermic process. In addition, the entropy change is also negative, thus confirming that the confined status is characterized by an entropic loss. Indeed, in order to confine polymeric chains in nanochannels, the surface interaction has to be exothermic so to balance the entropy loss in conformational rearrangements related to confined configurations. Indeed, the concentration equilibrium in the confining area, under the hypothesis of no interaction with the nanochannels, was predicted to be temperature independent19 and supposed to vary in the case of interaction with walls.16 Interestingly, over the temperature range investigated we found a linear dependence of the enthalpy variation on temperature, which is a striking indication of a constant value of ΔHi° with temperature changes. Moreover, by comparing the two slopes at the two molecular weights investigated, a linear dependency with polymerization grade is recovered. In particular, for PEG20 kDa a value of −44 ± 6 J/(mol K) is measured, while an almost double value of −93 ± 14 J/(mol K) is found for PEG40 kDa. This verifies the linear dependence on molecular weight of the interaction strength between polymer and surfaces giving −30.7 J/mol monomer unit. Such a result is usually expected for small molecules,32 but it is relevant for large macromolecules confined in nanoscopic space. Interestingly, scaling results can help in understanding the separation mechanism ongoing for partially adsorbed macromolecules under confinement after a temperature change. In equilibrium conditions, the free energy of binding for a confined chain of polymerization grade m weakly adsorbing on a surface is given by ΔGi° ∝ Tmδ2, where Tδ is the effective attraction seen by a monomer with the surface.12 The free energy is predicted to vary in a linear fashion when changing the temperature of the system. Indeed, in order to keep equilibrium conditions, m or δ should change. In particular, the effective interaction energy, δ, is evaluated for the single monomer unit and should not have large variations at different temperatures. From the experimental observations reported in Figure 6, a constant value of the interaction energy per monomer unit with the surface was inferred, which we assimilate with the constant value of δ with temperature variations. In these conditions, m must vary in order to recover static equilibrium and, in particular, should decrease for increasing T.14 Therefore, equilibrium conditions could be established again only for those confined macromolecules having a lower molecular weight when temperature is increased. In chromatography it is well recognized and widely exploited that temperature can affect the chromatographic regimes.14,33 By changing temperature below and above the critical temperature, the chromatographic mode would change from adsorptive to exclusion chromatographic, while at the critical temperature both molecules would elute in the same way. From the thermodynamic plot of Figure 6 we can infer that the critical temperature at which both compounds show the same partitioning is around 10 °C. This mechanism could then be also employed in nanofluidic structures. As a final remark, the possibility of modulating the separation regime with temperature is indeed proved at the molecular scale and is found in coherence with thermodynamic microscopic vision of weakly adsorbing single polymer chains.

uration is influenced by polymer solubility in water, polymer flexibility, polymer−surface interactions, polymer confinement extent, and corresponding reduction in configurational entropy. The measured reduction of the macromolecule size in solution with the temperature increase confirms their reduced solubility at temperatures closer to the spinodal point of about 100 °C for the water−PEG system. However, an issue related to changes in solubility should not affect changes in partitioning with temperature, since PEG interaction with water should be comparable for both the molecules in the confined space and those in the unconfined bulk at each temperature investigated. The measured size of unconfined PEG molecules was larger than the nanometric height of the nanoslit at all temperatures investigated. PEG macromolecules are highly flexible having a characteristic Khun segment length of about 1 nm28 and can enter the nanoconfined space even at a confinement extent larger than full occupancy against an entropic loss related to confined configuration. Confined macromoleculesin order to balance such energetic losshave to gain energy interacting with the confining area in the form of adsorption events. In addition, since PEG has a neutral charge, issues related to electrostatic interactions in the nanochannel can be discarded. As already mentioned before, changes in partitioning are related to changes in the free energy associated with the confining process. In particular, partitioning can be expressed as a function of the free energy variation between the confined and the unconfined state and of the temperature of the system

⎛ ΔG° ⎞ ⎟ K i = exp⎜ − ⎝ RT ⎠

(2)

Then, it can be computed ΔG°i ΔH °i ΔS°i =− + (3) RT RT R where ΔHi° and ΔSi° are the enthalpy and the entropy variations associated with the confining process expressed as the difference between the contributes associated with the nanoconfined and the bulk states, T is the temperature expressed in kelvin, and R the gas constant. In Figure 6, the ln K i = −

Figure 6. Diagram of thermodynamic parameters expressed as the logarithm of partitioning for both PEG20 and PEG40 kDa vs 1000/T.

dependence of free energy variations related to the confining process is reported against the inverse of temperature. Then, from slope and intercept of the plot of ln Ki versus 1/T, −ΔHi°/R and ΔSi°/R are derived. It is noticed that the thermodynamic plot of partitioning against the inverse of temperature shows a positive slope and then follows that the enthalpy variation associated with the confining process must 8758

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FCS Calibration. Precise evaluations of beam radius wxy and height wz are needed in the case of quantitative comparison of results obtained at different temperatures. Indeed, we measured the confocal volume size as a function of temperature in both bulk (NUNC cells) and nanoconfined setups. Focal volume dimensions were calculated from wxy2(T) = 4D(T)τdiff. Here, the diffusion time τdiff was fit from ACFs of RB dye diffusing in water to a 3D diffusion model

CONCLUSIONS The requirement of external forces to transport molecules, for example using hydrostatic or electrokinetic drive, results in limited microsystem design and application options. Recently, both entropy gradients and temperature gradients have been demonstrated to induce nanoconfined molecules migration in nanofluidics. In this study we demonstrate the possibility of separating macromolecules of neutral charge in borosilicate nanochannels by means of molecular confinement and temperature. These parameters directly affect the thermodynamic equilibrium and the partitioning of confined macromolecules in a size-dependent manner that allows the engineering of the nanospace for macromolecule separation of very few molecules. The identified thermodynamic equilibrium regulating the concentration change in the nanoconfined space can be employed to separate by size different molecules in devices operating on very few molecules. This could be easily implemented in lab on chip applications where temperature can be locally controlled. Indeed, in the frame of nanofluidics, our report sets a new strategy to allow macromolecules separation through a diffusion-based mechanism strictly related to the extent of confinement, and therefore to the entropy penalty associated with it, while others only address molecules manipulating in entropic or temperature gradient set.

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G(τ ) =

⎛ ⎞ 1 1 1 (1 + Θ)⎜ ⎟ ⟨N ⟩ ⎝ 1 + (τ /τdiff ) ⎠ 1 + s 2(τ /τdiff )

(4)

where ⟨N⟩ is the mean number of particles, Θ is expressed as θ/(1 − θ) exp(−τ/τT) where θ is the triplet kinetics fraction, τT the triplet time, and s the structure parameter, s = wz/wxy.. The reference diffusion coefficients at different temperatures for RB dye, D(T), were evaluated from

D(T ) = D(25 °C)

T 8.9 × 10−4 Pa·s η(T ) 298.15 K

(5) −6

2 −1 34

with η(T) the solvent viscosity and D(25 °C) = 4.3 × 10 cm s . Hydrodynamic properties of molecules in bulk were calculated by using the Stokes−Einstein equation D = kT/6πrhη, where k is the Boltzmann constant. The diffusion coefficient was evaluated from the diffusion time extracted from fitting procedures of the ACFs to the single component 3D model (see eq 4) following equation D(T) = wxy2(T)/4τdiff, where wxy(T) was fixed in temperature calibration shown in Figure 1. Θ parameters are kept fixed to the values found in bulk measurements for both dyes of θ = 0.34 ± 0.02 and τT =1.7 ± 0.1 μs and of θ = 0.40 ± 0.05 and τT = 5.0 ± 0.2 μs for RB and Cy5, respectively. FCS in Nanochannels. FCS was employed for the evaluation of macromolecular diffusion and concentration in nanometric slit channels. In such geometries the detection volume is confined to the height of the nanochannel, and the confocal volume is reduced to a cylinder of nanometric height; therefore, motion is perceived as a 2D diffusion process. Here further restrictions related to lateral boundaries are avoided.35 Macromolecule concentration within nanochannels was measured as Cnano = ⟨N⟩/Vnano where Vnano is the volume probed in nanochannels and ⟨N⟩ is the average number of molecules in the sampling volume. The confined sampling confocal volume, Vnano, was evaluated from the cylindrical shape obtained from calibrated waist size wxy and nominal channel height h of 10 nm (Vnano= πwxy2 × h). The number of molecules in the sampling volume was obtained from the inverse of the autocorrelation function at zero lag time and background corrected as ⟨N⟩ = 1/G(0)χ2 where χ = (1 + ⟨b⟩/(⟨F⟩ − ⟨b⟩), ⟨b⟩ being the average background intensity and ⟨F⟩ the average fluorescent intensity recorded.37 ⟨N⟩ was evaluated from fitting of the ACFs to eqs 6 and 7. Since small variation (less than 5%) were recorded between the values obtained from the two fitting models, results obtained from eq 6 were considered for further analysis (see Supporting Information). The diffusion time of macromolecules confined in the nanoslits was evaluated from fitting of the ACF to the anomalous diffusion model and the diffusion plus adsorption model. Briefly, for single species diffusing in 2D having a time dependence of the mean-square displacement (MSD) as MSD ∝ tα the ACF reads38

EXPERIMENTAL PROCEDURES

Borosilicate nanochannels (Micronit Microfluidics, Enschede, The Netherlands) 10 nm deep and 30 μm wide, with constant length of 500 μm, were preconditioned with Milli-Q (18 MΩ cm−1) water and then loaded by capillarity with a micromolar solution of fluorescent dyes (RB and Cy5, Sigma-Aldrich) and of PEG 20, 30, and 40 kDa functionalized with both RB and Cy5, neutral (Nanocs, New York). Channels are 10 nm deep and 30 μm wide, with constant length of 500 μm. Microcapillaries were adopted for solution loading and airtight connected by PEEK connectors at no residual flux conditions, and the system was let equilibrating overnight before measurements. Focus was positioned in correspondence of the maximum molecular brightness17 and performed in the middle of nanochannels to avoid laser beam lateral confinement.35 Each experiment was carried out at least 10 times to have statistical information in three different experimental cells at 23, 37, and 45 °C in a thermostat environment; temperature was controlled by a thermocouple in contact with the chip having ±1 °C uncertainty. The number of confined molecules was evaluated at 50 μm from nanochannel inlet at different time points, allowing 30 min of temperature equilibrium setting. A confocal fluorescence correlation spectroscope, ConfoCorII (Carl Zeiss, Jena, Germany), was used to carry out FCS experiments. RB was excited by laser light at 543 nm, while Cy5 at 633 nm. The laser beam was focused by an Apochromat 63× water immersion objective (numerical aperture 1.2). The emitted fluorescent light was collected by the same objective and separated from the excitation light by a dichroic mirror. The emission beam was mapped onto a pinhole in the image plane of the objective (80 μm). Fluorescent emission was sent to a 550-570BP or to a 650LP filter in correspondence of the two beam lengths and then acquired on the avalanche photodiodes (APDs). Fluorescence was detected by an APD in single-photoncounting mode. The system built-in correlator was employed for bulk measurements; a custom developed software (Fluctuation Analyzer) was dedicated to the analysis of all measurements in nanoconfinement. All ACFs were calculated directly from signal trajectories. To optimize computer performance, data were binned during analysis to 2 μs. The maximum lag time was set to 30 s for bulk measurements and to 180 s for nanochannel measurements. Averaging was performed over an acquisition period up to 40 min for macromolecules measurements via post-ACF calculation.

G(τ ) =

⎛ ⎞ 1 1 (1 + Θ)⎜ α⎟ ⟨N ⟩ ⎝ 1 + (τ /τdiff ) ⎠

(6)

A nonlinear dependence of the MSD on time is expressed by α ranging from 0 to 1, recovering the linearity for α = 1. The ACF model that accounts for diffusion as well as rare and strong adsorption events, having mean desorption time τDes, is given in eq 7

G(τ ) =

⎛ funbound ⎞ 1 (1 + Θ)⎜ + (1 − funbound )e−τ / τDes⎟ ⟨N ⟩ 1 + ( τ / τ ) ⎝ ⎠ diff (7)

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where f unbound represents the probability that a molecule in equilibrium is in the unbound state.39,40 In particular, τDes is equal to the inverse of the rate constant for desorption of adsorbed molecules and reflects the average time molecules spend adsorbed on the nanochannel walls. τdiff evaluated from eq 7 is adopted for calculation of the diffusion coefficient of confined molecules through D(T) = wxy2(T)/4τdiff, where wxy(T) was fixed in temperature calibration shown in Figure 1. In both equations triplet parameters were fixed to the values found in bulk measurements for both dyes.

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(20) Gorbunov, A. A.; Vakhrushev, A. V. J. Chromatogr., A 2005, 1064, 169−181. (21) Elson, E. L.; Magde, D. Biopolymers 1974, 13 (1), 1−27. (22) Wöll, D. RSC Adv. 2014, 4, 2447−2465. (23) Enderlein, J.; Gregor, I.; Patra, D.; Dertinger, T.; Kaupp, B. ChemPhysChem 2005, 6, 2324. (24) Sozański, K.; Wiśniewska, A.; Kalwarczyk, T.; Holyst, R. Phys. Rev. Lett. 2013, 111, 228301. (25) Hammouda, B.; Ho, D. L. J. Polym. Sci., Part B: Polym. Phys. 2007, 45, 2196−2200. (26) Hammouda, B.; Ho, D.; Kline, S. Macromolecules 2004, 37, 6932. (27) Tanford, C. Physical Chemistry of Macromolecules; John Wiley & Sons: New York, 1961. (28) Rubinstein, M.; Colby, R. H. Polymer Physics; Oxford University Press: New York, 2003. (29) Rigler, R.; Elson, E. L. Fluorescence Correlation Spectroscopy. Theory and Applications; Springer-Verlag: Berlin, 2001. (30) Wang, Y.; Teraoka, I.; Cifra, P. Macromolecules 2001, 34 (1), 127−133. (31) Scheutjens, J. M. H. M.; Fleer, G. J. The Effect of Polymers on Dispersion Properties; Tadros, Th. F., Ed.; Academic Press: London, 1982. (32) Martin, A. J. P. Biochem. Soc. Symp. 1949, 3, 4−20. (33) Chang, T.; Lee, H. C.; Lee, W.; Park, S.; Ko, C. Macromol. Chem. Phys. 1999, 200, 2188−2204. (34) Gendron, P.-O.; Avaltroni, F.; Wilkinson, K. J. J. Fluoresc. 2008, 18, 1093−1101. (35) Sanguigno, L.; De Santo, I.; Causa, F.; Netti, P. A. Anal Chem. 2010, 82 (23), 9663−9670. (36) Sanguigno, L.; De Santo, I.; Causa, F.; Netti, P. A. Anal Chem. 2011, 83 (21), 8101−8107. (37) Koppel, D. E. Phys. Rev. A 1974, 10 (6), 1938−1945. (38) Saxton, M. J. Biophys. J. 1996, 70, 1250−1262. (39) Wirth, M. J. Appl. Spectrosc. 2001, 55 (6), 663−669. (40) Wirth, M. J.; Legg, M. A. Annu. Rev. Phys. Chem. 2007, 58, 489− 510.

ASSOCIATED CONTENT

S Supporting Information *

Figures S1−S4 and Table R1. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail [email protected] (P.A.N.). Author Contributions

P.A.N. and I.D.S. conceived the idea. I.D.S. set up and performed experiments, analyzed data, and wrote the manuscript. I.D.S., F.C., and P.A.N. discussed the results and gave approval to the final version of the manuscript. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors thank Dr. J. Enderlein and Dr. L. Sanguigno for useful discussions and comments.

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REFERENCES

(1) Teraoka, I. Polymer Solutions: An Introduction to Physical Properties; John Wiley & Sons, Inc.: New York, 2002. (2) Desmet, G.; Eeltink, S. Anal. Chem. 2013, 85, 543−556. (3) Singhal, R.; Mochalin, V. N.; Lukatskaya, M. R.; Friedman, G.; Gogotsi, Y. Sci. Rep. 2012, DOI: 10.1038/srep00510. (4) Benítez, J. J.; Topolancik, J.; Tian, H. C.; Wallin, C. B.; Latulippe, D. R.; Szeto, K.; Murphy, P. J.; Cipriany, B. R.; Levy, S. L.; Soloway, P. D.; Craighead, H. G. Lab Chip 2012, 12, 4848−4854. (5) Han, J.; Craighead, H. G. Science 2000, 288, 1026. (6) van Dorp, S.; Keyser, U. F.; Dekker, N. H.; Dekker, C.; Lemay, S. G. Nat. Phys. 2009, 5, 347. (7) Wang, X.; Liu, L.; Pu, Q.; Zhu, Z.; Guo, G.; Zhong, H.; Liu, S. J. Am. Chem. Soc. 2012, 134, 7400−7405. (8) Stavis, S. M.; Geist, J.; Gaitan, M.; Locascio, L. E.; Strychalski, E. A. Lab Chip 2012, 12, 1164−1182. (9) Thamdrup, L. H.; Larsen, N. B.; Kristensen. Nano Lett. 2010, 10, 826−832. (10) He, Y.; Tsutsui, M.; Scheicher, R. H.; Bai, F.; Taniguchi, M.; Kawai, T. ACS Nano 2013, 7 (1), 538−546. (11) Casassa, E. F.; Tagami, Y. Macromolecules 1969, 2 (1), 14−26. (12) Daoud, M.; De Gennes, P. G. J. Phys. (Paris) 1977, 38, 85−93. (13) Cifra, P.; Bleha, T. Polymer 2000, 41 (3), 1003−1009. (14) Gorbunov, A. A.; Ya Solovyova, L.; Skvortsov, A. M. Polymer 1998, 39 (3), 697−702. (15) Teraoka, I.; Zhou, Z.; Langley, K. H.; Karasz, F. E. Macromolecules 1993, 26 (12), 3223−3226. (16) Cifra, P.; Bleha, T. Macromolecules 2001, 34 (3), 605−613. (17) De Santo, I.; Causa, F.; Netti, P. A. Anal. Chem. 2010, 82 (3), 997−1005. (18) Krutyeva, M.; Wischnewski, A.; Monkenbusch, M.; Willner, L.; Maiz, J.; Mijangos, C.; Arbe, A.; Colmenero, J.; Radulescu, A.; Holderer, O.; Ohl, M.; Richter, D. Phys. Rev. Lett. 2013, 110, 108303. (19) Krishnan, M.; Mönch, I.; Schwile, P. Nano Lett. 2007, 7 (5), 1270−1275. 8760

dx.doi.org/10.1021/ma501827z | Macromolecules 2014, 47, 8754−8760