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Adsorption and denaturation of structured polymeric nanoparticles at an interface Chang Tian, Jie Feng, H. Jeremy Cho, Sujit Datta, and Robert K Prud'homme Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.8b01434 • Publication Date (Web): 05 Jul 2018 Downloaded from http://pubs.acs.org on July 5, 2018
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Nano Letters
Adsorption and denaturation of structured polymeric nanoparticles at an interface Chang Tian&, Jie Feng&, H. Jeremy Cho, Sujit S. Datta and Robert K. Prud’homme* Department of Chemical and Biological Engineering, Princeton University, Princeton, New Jersey, 08544, United States Abstract: Nanoparticles (NPs) have been widely applied in fields as diverse as energy conversion, photovoltaics, environment remediation, and human health.1 However, the adsorption and trapping of NPs interfaces is still poorly understood and few studies have characterized the kinetics quantitatively. In many applications, such as drug delivery, understanding NP interactions at an interface is essential to determine and control adsorption onto targeted areas.2. Therapeutic NPs are especially interesting because their structures involve somewhat hydrophilic surface coronas, to prevent protein adsorption, and much more hydrophobic core phases. We initiated this study after observing aggregates of nanoparticles in dispersions where there had been exposure of the dispersion to air interfaces. Here, we investigate the evolution of NP attachment and structural evolution at the air-liquid interface over time scales from 100 milliseconds to 10s of seconds. We document three distinct stages in NP adsorption. In addition to an early stage of free diffusion and a later one with steric adsorption barriers, we find a hitherto unrealized region where the interfacial energy changes due to surface “denaturation” or restructuring of the NPs at the interface. We adopt a quantitative model to calculate the diffusion coefficient, adsorption rate and barrier, and extent of NP
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hydrophobic core exposure at different stages. Our results deepen the fundamental understanding of the adsorption of structured NPs at an interface.
Key words: Nanoparticle, denature, dynamic surface tension, interface, maximum bubble pressure, block copolymer
TOC Graphic:
Main text: The kinetics of NP surface adsorption are investigated by measuring the change of dynamic surface tension (DST) throughout the adsorption process using a maximum bubble pressure tensiometer (MBPT). NPs of solid polystyrene (PS) core or liquid Vitamin E (VE) core and polyethylene oxide (PEO) corona were made using the Flash NanoPrecipitation (FNP) method.3 PEO of two molecular weights were used to stabilize the NPs to explore the role of the stabilizing polymer relative to the core: 2.6k and 5k PEO, to produce coronas with thicknesses of 8 nm and 15 nm, respectively. NPs made with PS core and 2.6k PEO (NPPS3k), PS core and 5k PEO (NPPS5k), VE core and 5k PEO (NPVE5k) had an average diameter of 55, 75, 75 nm, respectively. The
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characteristic time for NPs to diffuse to the interface is in the order of 0.1 s (See SI5), below the typical working time of surface tension measuring devices such as a pendant drop tensiometer or Wilhelmy plate.4,5 Therefore, we use the maximum bubble pressure tensiometer (MBPT),6,7 which is able to capture the DST change in the early time regime of 0.1 s.8 An illustration of the MBPT set-up is shown in Figure 1(A). Figure 1(B) shows the DST change for NPPS5k of different concentrations over times from 0.1 second to 30 second. In Figure 1(C), the curves are superimposed horizontally along the time axis to show a universal behavior for all concentrations. The decrease in surface tension occurs in three stages. We provide a physical explanation, and a mathematical model for each stage.
Figure 1. (A) Schematic of the Maximum Bubble Pressure Tensiometer (MBPT). The flow rate of gas through the capillary is adjusted to vary the time, t, to achieve the maximum pressure difference (∆ ), which occurs when the bubble radius equals the capillary radius. From the maximum pressure, the dynamic surface tension (DST) at this time t is calculated. (B) Surface tension over time for different concentrations Cm ( : 0.05; : 0.1; : 0.2, : 0.4; : 0.8; : 1.2; : 1.6; : 2; All unit in mg/mL) of NPPS5k, plotted in a semi-logarithm scale. Corresponding plots for NPPS3k and NPVE5k can be found in SI2. (C) Curves from (B) shifted horizontally with respect to the data at Cm = 0.4 mg/mL, indicating the time:concentration superposition of surface tension. The shifting factors, a, scale as C-2, are shown in SI Figure 2(b). Three stages of behavior are displayed.
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At very early times
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, NPs diffuse to the pristine interface, which acts as a
perfect sink with no barriers to adsorption. Hence the diffusion-only Ward and Tordai mechanism9 is applicable. NPs larger than 10 nm have adsorption trapping energy exceeding 103 kBT.10 Bizmark et al.11 modified the Ward and Tordai model to account for the surface tension change at small fractional surface coverage (θ) in the early stages. |∆ |
where
is the pure liquid surface tension,
is Avogadro’s number,
is molar
concentration of NPs. We calculate the mass of a NP using the Alexander-de Gennes model, with the Daoud and Cotton correction12 for surface curvature13 (see SI3). The molar NP concentration is calculated from this model using the mass concentration of NPs. The number of NPs adsorbed at the interface is much less than that remaining in the bulk, therefore,
is assumed to be constant throughout the adsorption process.
is the Stoke-Einstein diffusion coefficient of the NPs. For NP transport to an interface at very low surface coverage ( ), the adsorption barrier is not yet significant, so Eqn. 1 can be applied. We calculate the actual diffusion coefficient (DEstimate) of NPs based on Eqn. 1 with the estimated first-stage adsorption energy |∆EEstimate1|. Then we prove that Eqn. 1 is valid in stage 1 by comparing DEstimate with DSE, which are shown to be similar. (See SI6 for the calculation). Surface coverage at any time during adsorption ( ) is calculated from the measured surface tension11
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where
is the ultimate surface coverage, which is 0.91 for hexagonal close packing of
spherical NPs at the interface14, MBPT and
is the pristine surface tension of water measured by
is the equilibrium surface tension corresponding to
Eqn. S13 for calculation). The value tension of the aqueous interface at
0.91 (see SI
is a hypothetical value for the final surface 0.91 without any structural rearrangement
(which occurs during stage 2).
Figure 2.(A) For all three NPs, two linear regimes with different gradients were obtained using the early stage approximation. Points represent experiment data, and solid lines show the observed trends. (B) Surface tension over time, of 0.4 mg/mL NPPSs using two different BCPs and their corresponding PEO solution with the same mass concentration and similar PEO molecular weight. The surface tension for NPs decreases more slowly compared to that of PEO at start, but reaches a lower ultimate surface tension. (C) The non-dimensional master curve for the stage 2 of NP denaturation. This accounts for different concentration of all three NPs.
In Bizmark et al.’s early stage approximation, observed when DST was plotted against
.
.3, only one slope was
. However, in Figure 2(A) we observe two
clearly different straight lines of DST against t
.
. The transition between two stages
happens at an earlier time for NPs with 5k PEO brushes compared to NPs with 3k
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brushes. No statistically significant difference of surface tension was observed for the transition point of all three types of NPs we tested. For the first stage, we calculate the adsorption energy per surface area of the three types of NPs using the slope of the DST over
.
in Eqn. 1. As listed in Table 1, NPs with a 2.6k PEO brush have similar
adsorption energy per area as NPs with a 5k PEO brush, as they have similar PEO density in the NP corona (see SI4 for calculation of PEO corona density). However, for the second stage, a much larger slope of DST versus
.
was observed. We calculated
the ending surface coverage of stage 1 (θEnd1) based on the measured final surface tension
!"#$
of the first linear regime when
is plotted against
.
. For NPs of different
formulations and concentrations, θEnd1 is very similar. Moreover, θEnd1 is less than . %, hence the Stokes Einstein equation gives a good estimate of the diffusion coefficient of individual NPs during the second stage. The transition to stage 2 is attributed to an increase of adsorption energy |∆ |. The new adsorption energy |∆ | per NP for the beginning of the second stage is calculated by fitting the second stage slope of surface tension over t0.5. The results are shown in Table 1.
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Table 1. θEnd1 is NP surface coverage at the end of stage 1. |∆EStage1| and |∆EStage2| are adsorption energy of each stage. DSE is the calculated Stoke-Einstein diffusion coefficient. ka is the adsorption constant.
To account for this increase of |∆ |, we propose the following mechanism for stage 2. The structured NPs have a hydrophilic PEO corona and a hydrophobic PS or Vitamin E core. When we use Eqn. 2 to calculate |∆ | in stage 1, we assume the NPs to be PEO spheres so that only the PEO corona contacts the interface to decrease surface energy. To compare the surface adsorption of NPs to that of free PEO, we conducted the following experiments. We calculated the mass concentration of PEO for 0.4 mg/mL of both PSNP3k and PSNP5k (see SI1 for the formulation of those NPs). PEG (polyethylene glycol, which is chemically identical as PEO) of similar length was dissolved in the same mass concentration of PEO brushes as that in the corresponding NP solutions. DST was measured for those PEG solutions and compared with that of their corresponding NPs. As shown in Figure 2(B), in short time the surface tension of PEG decreases much faster compared to that of NPs, as expected, since PEG is of much smaller size (See SI7) compared to NPs. However, from approximately 1 s of adsorption onwards, the rate of decrease of surface tension for NPs is much faster compared to that of PEO, eventually leading to even lower equilibrium surface tensions. " ACS Paragon Plus Environment
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Should NPs stay as rigid PEO spheres at the interface, they would have higher equilibrium surface tension, as their surface coverage would be less compared to that of smaller and more closely-packed free PEO polymers at early times. Therefore, the more hydrophobic PS cores were exposed on the interface. Previously, Huang et al.15 studied the jamming of pH responsive NP-surfactants at the interface. PS NPs with ends of carboxylate groups are charge-dispersed when pH>5, but are jammed at lower pH. The transition is driven by electrostatic repulsions. However, the hydrophilic corona rearrangement and hydrophobic core exposure of our PS NPs are fundamentally different from this pH-triggered process. The NPs we consider, with PEG coronas, are not pH sensitive, and the DST for these NPs are independent of pH from 3.5 to 12.8 (see SI12). The newly observed two-stage transition for these synthetic NPs, is analogous to protein denaturation at an interface.16 A protein has hydrophilic groups on its surface that make it water soluble but hydrophobic peptide residues in the core. Our NPs have hydrophilic PEG coronas and hydrophobic cores. Proteins denature at a hydrophobic interface wherein the hydrophobic core peptides unfold at the interface, while the hydrophilic peptides still orient towards the aqueous phase. In SI9 we applied the Ward and Tordai analysis on the DST results of Beverung et al.16 for Bovine Serum Albumin (BSA) protein adsorption in the first two stages, which are characterized as “initial adsorption” and “denaturation of adsorbed proteins”. The values for energies and coverages are similar to the results for the PEG NPs reported here (see Table 1 and SI9). We borrow the term “denaturation” from protein unfolding, to describe this corona rearrangement of NPs leading to hydrophobic core exposure at the interface. This is not
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a strict translation of biological denaturation, and we will refer to this second stage as “restructuring” of the NP at the interface.
Figure 3. A schematic illustration of (A) ) , when the NPs first arrive at the interface. (B) ( , is the time required for a particle to denature at the interface. (C) At & # # time ' & ( # , NPs at the interface denature. Hence, the adsorption energy at interface is the energy difference between that of pristine surface and surface with denatured particles. The mechanism of NP surface denaturation, or restructuring, is illustrated in Figure 3. It takes
&
for NPs to diffuse to the interface and
#
to denature at the interface.
The onset of the change in slope of the surface tension curve corresponds to the denaturation time period
#,
#.
As '
&
(
#,
NPs continue to arrive at the interface, reside for a
and then denature. Hence the average adsorption energy change per NP
(|∆ |), is that of denatured NPs at the longer time. The surface energy of both PS and VE are ~35 mN/m,17,18 which are much lower compared to that of PEO; the exposed core decreases the surface tension for the denatured NPs compared to the initial reduction in surface tension from just PEO at the interface. The percentage increase of adsorption energy due to denaturation also varies based on the formulation of the NPs. As shown in Table 1, the denaturation stage of NPPS3k NPs happens much later from the start of adsorption compared to NPs with 5k PEO on the corona; there is also a $ ACS Paragon Plus Environment
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much more significant increase of adsorption energy due to denaturation for NPPS5k and NPVE5k compared to NPPS3k. These observations imply that NPPS3k takes a longer time to denature at the interface, and the energy change upon denaturation is more modest. The difference between the adsorption energies is consistent with the balance of anchoring energy of the PS block, relative to the energy associated with compression of the PEO hydrated chain at the interface. This anchoring energy argument is incorporated in models of block copolymer micellization by Leibler19 and PEG osmotic compression energy by Hansen.20 That balance, which determines the “net anchoring energy”, has two predominant terms. The first is the energy associated with the hydrophobic block creating interface with the aqueous phase; that energy keeps the block copolymer anchored. The second energy is associated with the hydrophilic PEG block. That block is laterally compressed because of its interactions with other PEG blocks. That osmotic pressure (due to the PEG chains in the corona that are in the aqueous phase) provides an energy that would expel the block copolymer from the interface. The higher Mw PEG is more compressed than the lower Mw PEG block (5k versus 3k PEG) as we have recently shown by NMR measurements on our NPs.13 Consequently, the higher osmotic pressure in the corona that would tend to expel the block copolymer from the interface. The hydrophobic anchoring energy is the same from both hydrophobic blocks, but the energy associated with osmotic pressure is greater for the larger PEG. Therefore, the net “anchoring energy” is less for the larger PEG block. NPs with same PEO brush length, NPPS5k and NPVE5k, have similar adsorption energies in the first stage, as that is essentially PEO adsorption. Their adsorption energies are also similar in the second stage. This indicates that the core
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materials of similar surface energy (PS versus Vitamin E) lead to similar adsorption energy after hydrophobic core exposure. We modified Eqn. 1 to give a quantitative description of DST change in stage 2: *∆
!"#$
where
!"#$
+, -./ *
0 1√
3
is the ending surface tension of stage 1 and
+, -.$ 4 +, -.$
3
is the total time duration
of stage 1. !"#$
5/
+, -.$ !"#$
6
/
is the ending surface coverage of stage 1. Both
!"#$
and
!"#$
are similar in
value among NPs of different formulations and concentrations. Based on the above understandings, we further collapse the stage 2 of all NPs across different concentrations into one master curve using Eqn. 1. We arrange Eqn. 1 into a non-dimensional form based on different stages for each NP formulation. 7 !"#$
7
( 6
*∆
8
+, -./ *
*∆
?.@ AA
B ,.@ CB ,.@
,.@ H CD!E IJK CF>@. are
(
D!E CD!E
(
F>@. CF>@.
G
the fraction of interface occupied by water, PEO and the
hydrophobic core, respectively. The surface tension of core material PS and VE D+
L
M!
38 NOPN. QD!E is the surface tension of PEO as the coronas of the NPs,
which is calculated based on the adsorption energy for un-denatured NPs from the first stage of adsorption (See SI6). We assume that the crowded PEO surface segment density does not change significantly after NP denaturation. In addition, stage 2 is based on the free diffusion analysis of single NPs, where Bizmark et al. found that the early free-diffusion stage ends at
= 0.3.11 Therefore we assume CD!E ( CF>@.
the end of stage 2. Using Eqn. 8, at the end of stage 2, CF>@.
.3 at
6% for NPPS3k, 10% for
NPPS5k and 8% for NPVE5k. The larger hydrophobic surface exposure by NPPS5k compared to NPPS3k is consistent with the lower net anchoring energy of the PS block for the 5k PEG. This result provides us with an estimation of the extent hydrophobic
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core exposure and a possible direction on adjusting the extent of NP denaturation based on length of the corona chain. The displacement of the PEG corona to expose the more hydrophobic core to the interface creates the dramatic change of DST in stage 2. In response to a question from a reviewer, we have conducted a complementary experiment to directly visualize NP interfacial restructuring by measuring mass transfer of a hydrophobic dye from the NP core across an interface. The experiment is described in detail in the SI13, and the results confirm our proposed mechanism of NP denaturation at the interface. As shown in Figure 4(A), we follow the later-stage Ward and Tordai P
approximation and plot DST over
.
for stage 3, where the surface adsorption of
NPs and exposure of hydrophobic cores at the interface slow down due to steric barrier. A linear fit was observed. Adamczyk proposed the following equation to account for the adsorption barrier at high NP surface coverage.22 R$
√ R$
S
T 5 / U VW
where c = 2.3 for hard spherical NPs (see SI10), VW is the bulk NP number
concentration. U is the later stage adsorption constant. We assume that c = 2.3 can also be applied to our core-corona structured NPs, provided that the PEO brushes are closely packed (see SI Table. S2) and less than 10% hydrophobic exposure is observed at the end of stage 2. Substituting Eqn. 2 into Eqn. 9, we have the following equation for DST at later stage.
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(
R$
√
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To compare the effect of the core materials and the corona molecular weight, for all three types of NPs, we calculate the adsorption constant UX from the gradient of DST over
P
.
at the later stage. The values of UX for all NPs are listed in Table 1. Clearly,
NPs with 5k PEO brushes have much larger adsorption constant UX compared to NPs
with 3k PEO brushes. This larger value of UX for 5k PEO NPs denotes a faster flux in stage 3 (see SI Eqn. S18), which is consistent with the larger adsorption energy calculated for 5k PEO NPs compared to 3k PEO NPs. Similar to the first two stages, Eqn. 11 is rearranged into:
where, 7Y
Z
7Y ( 9
[\ ] [^ / ` _ /a;bc d^ f h [\ e g \
3
The later stage DST change with respect to dimensionless time 7Y Pt for all three NPs across different concentrations is successfully collapsed into one master curve, as shown in Figure 4(B). This non-dimensional master curve is useful to predict DST change of core-shell particles of known structure in the later stage of adsorption (See SI10 and SI11 for further calculation of adsorption barriers using the calculated adsorption constant ka).
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Figure 4. (A) Plot of surface tension over (1/t)0.5 for 1.6 mg/mL of NPPS3k and NPPS5k. Linear regimes were observed. (B) The collapsed master curve for all three NPs in the third stage. In both figures, points represent experiment data, and solid lines represent the observed trends. In summary, we have monitored the dynamic surface tension with maximum bubble pressure tensiometer, to follow the adsorption of structured NPs from the bulk aqueous phase to the air-water interface. The measurements are interpreted with a modified Ward and Tordai model. In addition to an early stage of diffusion-dominated NP adsorption up to 6% of surface coverage and a final stage of adsorption at a NPladen interface, a transition stage due to structural rearrangement of NPs at the interface (i.e. the displacement of PEG corona and exposure of the hydrophobic core), is observed for the first time. This structural change for these synthetic structured NPs has parallels with protein denaturation at interfaces and, in that sense, this is biomimetic. Our findings of the soft polymeric NP adsorption and denaturation offer new insights for the interfacial behavior of NPs at the interface. The mathematical model and mechanism we developed provide a quantitative understanding of phenomena
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associated with the adsorption-driven dynamics of structured polymeric nanoparticles at interfaces.
Methods:
Materials: Polystyrene, block co-polymer (BCP) polystyrene 1.6kDa-b-poly(ethylene oxide) 5kDa and polystyrene 1.9kDa-b-poly(ethylene oxide) 2.6kDa were from Polymer Source Inc. (Dorval, QC, Canada). α-Tocopherol (Vitamin E) was from Sigma-Aldrich. Polyethylene oxide 5kDa was purchased from Research Organics Inc. (Cleveland, OH) and polyethylene oxide 2.2kDa was purchased from Sigma-Aldrich. All materials are used per received. The MQ water was purified by a 0.2µm filter and four-stage deionization to a resistivity of more than 17.5 MΩ (Nanopore Diamond from Barnstead).
NP synthesis and characterization: NPs were synthesized using the Flash NanoPrecipitation method. 10 mg/mL of hydrophobic core materials and 10 mg/mL of BCP were dissolved in 1 mL tetrahydrofuran stream and rapidly mixed with 1 mL water stream in the Confined Impinging Jet (CIJ), the product was further diluted by 8 mL additional water reservoir. More information on the working mechanism of CIJ can be found in works by Johnson et al.3 and Saad et al.23,24 The resulting NP solution was placed in Spectra/Por 1 dialysis membrane of MWCO 6-8 kDa and dialyzed for 18 hours. The dialysis water was changed twice. NP intensity-weighted size distribution was measured by dynamic light scattering (DLS) using a Zetasizer Nano-ZS (Malvern Instrument, Malvern, UK) with the normal mode analysis program. %! ACS Paragon Plus Environment
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Dynamic surface tension measurement: We used the maximum bubble method to measure the dynamic surface tension change within 33 seconds of interface formation. 20 mL of NP solution was added to a cylinder glass vessel with a bottom diameter of 40 mm. The surface tension of the solution was determined using a maximum bubble pressure tensiometer (BP100) from Krüss (Hamburg, Germany). The temperature of the experiment chamber was kept at 24 ± 1 oC. The surface tension of water was measured before each new sample, in order to ensure the accuracy of the measurement. The Teflon capillary of BP100 was washed with acetone and MQ eater before each measurement, followed by nitrogen purge. Experimental data were recorded using Krüss Laboratory Desktop software. The surface tension data below first 0.1 seconds was not used in subsequent calculations due to the inertia effects on bubble formation. The surface tension of α-tocopherol (Vitamin E) was measured using a drop weight method.25 A syringe filled with α-tocopherol was connected to a stainless-steel capillary with a 90o angle. The total mass of multiple liquid droplets was measured on a balance.
Acknowledgement: We would like to thank Johnson & Johnson for providing us the access of the maximum bubble pressure tensiometer (BP100).
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Reference: (1) (2)
(3)
(4) (5)
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(8) (9) (10)
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(12) (13)
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Petros, R. A.; Desimone, J. M. Strategies in the Design of Nanoparticles for Therapeutic Applications. Nat. Rev. Drug Discov. 2010, 9, 615–627. Nie, Z.; Petukhova, A.; Kumacheva, E. Properties and Emerging Applications of Self-Assembled Structures Made from Inorganic Nanoparticles. Nat. Nanotechnol. 2009, 5 (1), 15–25. Johnson, B. K.; Prud’homme, R. K. Flash NanoPrecipitation of Organic Actives and Block Copolymers Using a Confined Impinging Jets Mixer. Aust. J. Chem. 2003, 56 (10), 1021–1024. Miller, R.; Makievski, A. Fundamentals of Interfacial Science. SINTERFACE Technol. 2011, 7 (D-12489). Eastoe, J. U.; Dalton, J. S. Dynamic Surface Tension and Adsorption Mechanisms of Surfactants at the Air-Water Interface. Adv. Colloid Interface Sci. 2000. Christov, N. C.; Danov, K. D.; Kralchevsky, P. A.; Ananthapadmanabhan, K. P.; Lips, A. Maximum Bubble Pressure Method : Universal Surface Age and Transport Mechanisms in Surfactant Solutions. Langmuir 2006, No. 29, 7528– 7542. Fainerman, V. B.; Miller, R.; Joos, P. The Measurement of Dynamic Surface Tension by the Maximum Bubble Pressure Method. Colloid Polym. Sci. 1994, 739, 731–739. Miller, R.; Liggieri, L. Bubble and Drop Interfaces; CRC Press, 2011. Ward, A. F. H.; Tordai, L. Time-Dependence of Boundary Tensions of Solutions I. The Role of Diffusion in Time-Effects. J. Chem. Phys. 1946, 14, 453–461. Zell, Z. A.; Isa, L.; Ilg, P.; Leal, L. G.; Squires, T. M. Adsorption Energies of Poly(Ethylene Oxide)-Based Surfactants and Nanoparticles on an Air − Water Surface. Langmuir 2014. Bizmark, N.; Ioannidis, M. A.; Henneke, D. E. Irreversible Adsorption-Driven Assembly of Nanoparticles at Fluid Interfaces Revealed by a Dynamic Surface Tension Probe. Langmuir 2014, 30 (3), 710–717. Daoud, M.; Cotton, J. P. Star Shaped Polymers : A Model for the Conformation and Its Concentration Dependence. J. Phys. 1982, 43, 531–538. Pagels, R. F.; Edelstein, J.; Tang, C.; Prud’homme, R. K. Controlling and Predicting Nanoparticle Formation by Block Copolymer Directed Rapid Precipitations. Nano Lett. 2018, acs.nanolett.7b04674. Du, K.; Glogowski, E.; Emrick, T.; Russell, T. P.; Dinsmore, A. D. Adsorption Energy of Nano- and Microparticles at Liquid - Liquid Interfaces. Langmuir 2010, 26 (23), 12518–12522. Huang, C.; Sun, Z.; Cui, M.; Liu, F.; Helms, B. A.; Russell, T. P. Structured Liquids with PH-Triggered Reconfigurability. Adv. Mater. 2016, No. 28, 6612–6618. Beverung, C. J.; Radke, C. J.; Blanch, H. W. Protein Adsorption at the Oil/Water Interface: Characterization of Adsorption Kinetics by Dynamic Interfacial Tension Measurements. Biophys. Chem. 1999, 81 (1), 59–80. Wu, S. Estimation of the Critical Surface Tension for Polymer from Molecular Constitution by a Modified Hildebrand-Scott Equation. J. Phys. Chem. 1968, 3 (7), %# ACS Paragon Plus Environment
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Stage 1 (SE diffusion) 1 2 3 4 5 6 7 8 9 10 11 12 13 14
Nano Letters
Stage 2 (Denaturation)
Page 20 of 24 Stage 3 (significant adsorption barrier)
θEnd1
DSE × 1012 (m2s-1)
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