Coassembly of Poly(N-isopropylacrylamide) - ACS Publications

Article Cite This: Macromolecules XXXX, XXX, XXX−XXX

pubs.acs.org/Macromolecules

Coassembly of Poly(N‑isopropylacrylamide) with Dodecyl and Carboxyl Terminal Groups with Cationic Surfactant: Critical Comparison of Experimental and Simulation Data Anastasiia Fanova,† Karel Š indelka,† Mariusz Uchman,† Zuzana Limpouchová,*,† Sergey K. Filippov,‡ Stergios Pispas,§ Karel Procházka,*,† and Miroslav Š těpánek*,†

Downloaded via UNIV OF SOUTH DAKOTA on September 12, 2018 at 19:36:45 (UTC). See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.

†

Department of Physical and Macromolecular Chemistry, Faculty of Science, Charles University, Hlavova 2030, 128 40 Prague 2, Czech Republic ‡ Institute of Macromolecular Chemistry, Academy of Sciences of the Czech Republic, Heyrovský Sq. 2, 16206 Prague 6, Czech Republic § Theoretical & Physical Chemistry Institute, National Hellenic Research Foundation, 48 Vassileos Constantinou Avenue, 11635 Athens, Greece S Supporting Information *

ABSTRACT: Comicellization of poly(N-isopropylacrylamide) with dodecyl and carboxyl terminal groups (mPNIPAm) with cationic surfactant N-dodecylpyridinium chloride was studied by scattering techniques (light scattering, SAXS), isothermal titration calorimetry, fluorescence spectroscopy, and coarse-grained simulations using dissipative particle dynamics (DPD) as a function of charge ratio of N-dodecylpyridinium (DP+) ions to mPNIPAm terminal carboxylate groups, Z = [DP+]/[COO−]. While both experimental results and DPD data indicate that up to Z = 2 tails of the surfactant enter and swell the dodecyl core of mPNIPAm micelles, the further increase in the size of the core for Z > 2 caused by the dehydration and collapse of inner parts of PNIPAm chains observed by SAXS is not reproduced by DPD simulations. Nevertheless, the study demonstrates that the simplified coarse-grained model can account for hydrogen bonding and elucidate the mechanism of comicellization. The study shows that the electrostatic interactions modify appreciably the behavior of mPNIPAm, but the assembly with cationic surfactant is governed by hydrophobic interactions.

■

INTRODUCTION Poly(N-isopropylacrylamide) (PNIPAm) is one of the most extensively studied thermoresponsive polymers.1−3 As a polymer which is biocompatible4 and water-soluble at room temperature but insoluble at body temperature, PNIPAm is suitable for various stimuli-responsive drug deposition or drug delivery systems, such as polymer gels5,6 or nanoparticles.7,8 The phase transition at the lower critical solution temperature (LCST) is a result of dehydration of PNIPAm structural units. It reflects the temperature-induced redistribution of hydrogen bonds among pairs of PNIPAm units and water. LCST of PNIPAm depends on its molar mass (increasing with decreasing Mw) and also on its architecture. PNIPAm stars have a lower LCST than the linear PNIPAm.9 It was reported that the inner part of the PNIPAm multiarm stars collapses at a lower temperature than the outer part.10 The LCST of PNIPAm also increases upon the attachment of hydrophilic terminal groups and decreases upon the introduction of hydrophobic ones.11 Block copolymers consisting of a PNIPAm block and a hydrophilic block form micelles with PNIPAm cores in aqueous solution above the LCST. If the other block is hydrophobic, the copolymer forms micelles with PNIPAm shells in aqueous solutions at ambient temperatures. In this © XXXX American Chemical Society

case, the heating of micellar solutions above the LCST leads to the collapse of dehydrated micellar shells, but the phase separation of micelles proceeds much slower than in the case of PNIPAm homopolymer.12 The micelles are stabilized kinetically due to a high activation energy barrier which hinders mutual interpenetration of the dense micellar shells of different associates.13 The chain density of the PNIPAm shell depends on the length of PNIPAm blocks and strongly affects the temperature-responsive behavior of the micelles which results in the hysteresis of the cloud point curves.14 It was also reported that the kinetics of the growth of micellar associates with PNIPAm shells is controlled by structural rearrangement of the associates.15,16 Recently, a PNIPAm polymer with dodecyl and carboxylic terminal groups (C12-PNIPAm-COOH) was synthesized by RAFT polymerization using S-1-dodecyl-S′-(α,α′-dimethyl-α″acetic acid)trithiocarbonate as a chain transfer agent, and it was shown that it forms micelles in aqueous media with the core formed by the dodecyl terminal groups and having carboxylate terminal groups in the shell periphery.17 The modified Received: June 3, 2018 Revised: August 23, 2018

A

DOI: 10.1021/acs.macromol.8b01161 Macromolecules XXXX, XXX, XXX−XXX

Article

Macromolecules

where the polymer concentration was 5 mg/mL. The DAF concentration for fluorescence measurements was 4 μM. Methods. Light Scattering. LS measurements were performed with an ALV photometer consisting of a He−Ne laser, operating at the wavelength λ = 632.8 nm, an ALV CGS/8F goniometer, an ALV High QE APD detector, and an ALV 5004 multibit, multitau autocorrelator. The cell housing was connected to an external circulation thermostat keeping the constant temperature with the accuracy of ±0.1 °C. The temperature dependences were measured after heating and equilibration for 7−10 min. The measurements were performed at the scattering angle, θ = 90°. Dynamic light scattering measurements were evaluated using the CONTIN method. Zeta Potential. Electrophoretic mobility measurements were performed with a Nano-ZS Zetasizer (Malvern Instruments, UK). The obtained values were averages of ten subsequent measurements, each of which consisted of 15 runs. The ζ-potential values were calculated from electrophoretic mobilities using the Henry equation in the Smoluchowski approximation, μ = εζ/η, where μ is the electrophoretic mobility and ε is the dielectric constant of the solvent. Fluorescence Spectroscopy. Fluorescence spectroscopy measurements using DAF as an amphiphilic fluorescent probe were carried with a Fluorolog FL 3-22 fluorometer (Horiba Jobin Yvon, France) equipped with double grating excitation and emission monochromators and a FluoroHub time-correlated single photon counting module for emission decay measurements. Emission decays were measured in a time window of 50 ns with the resolution of 6.98 ps per channel using a 472 nm NanoLED pulsed laser diode source operated at a repetition frequency of 1 MHz. The decays were fitted by the micellar quenching model19 using Horiba DAS6 software performing the iterative reconvolution of the fitted model with the instrument response function by means of the Marquardt−Levenberg leastsquares algorithm. Small-Angle X-ray Scattering (SAXS). SAXS experiments for samples were performed on the high brilliance beamline ID0220 at ESRF (Grenoble, France) in 2 mm flow-through quartz capillaries at sample-to-detector distances 2 and 8 m, using a monochromatic incident X-ray beam with the energy, E = 12.46 keV, corresponding to q vectors from 0.05 to 2.76 nm−1. The SAXS setup utilized a pinhole camera with a beam stop placed in front of a two-dimensional Rayonix MX170-HS high-sensitivity low noise CCD detector having an active area of 100 × 100 mm2, which was divided into 512 × 512 pixels with 4 × 4 binning for the sample-to-detector distance 2 m and into 1024 × 1024 pixels with 2 × 2 binning for 8 m. Online corrections were applied for the detector, and the sample-to-detector distance, center, transmission, and incident intensity were calibrated. Ten or 20 frames with the accumulation time of 10 ms were taken and inspected for radiation damage. The frames without the presence of radiation damage were azimuthally averaged to determine the dependence of the scattered intensity I(q) on the scattering vector q. The calibration to absolute units (cm−1) was performed by dividing the scattered intensity by the thickness of the flow-through capillary (2 mm). The scattering from a capillary filled with 0.01 M sodium hydroxide was measured as a background and subtracted from the scattering intensity of the samples. The data were fitted to the model described in the Supporting Information using the SASfit 0.94.7 software.21 Isothermal Titration Calorimetry. ITC experiments were performed using a Nano ITC isothermal titration calorimeter (TA Instruments-Waters LLC, New Castle, DE). The measurements were performed at 25 °C. The instrument was equipped with a 24 karat gold reference cell and a cell for the sample with a volume of 183 μL. The sample cell was connected to a 50 μL syringe, which also ensured continuous mixing of the solutions in the cell rotating at 250 rpm. Titrations were performed by consecutive 1.01 μL injections of 50 or 100 mM aqueous DPCl solution into water and into 5 mg/mL (41.6 mM of monomer units) polymer aqueous solution with 300 s delay between them. Data were analyzed using the NITPIC software.

mPNIPAm polymer (mPNIPAm) does not undergo phase separation above the LCST of PNIPAm if carboxylic groups in the peripheral part of the micellar shell are ionized. Our recent study showed that the cloud point temperature of mPNIPAm increases with the increasing degree of ionization of carboxylate groups.18 This paper is the continuation and substantial extension of our previous study18 of pH-dependent thermoresponsivity of mPNIPAm. Instead of changing the degree of ionization of terminal carboxyl groups, we tune the net charge of mPNIPAm micelles by comicellization of the polymer with the cationic surfactant N-dodecylpyridinium chloride, DPCl. The comicellization of mPNIPAm with DPCl is studied by experimental techniques (light scattering, SAXS, fluorescence spectroscopy, and ITC) and by dissipative particle dynamics (DPD). The simulations are based on a simplified, albeit physically sound model, which reflects the effect of short-range nonelectrostatic interactions and the effect of long-range electrostatic interactions (including the indirect entropy effect of counterions). We would like to stress that by simulation we study the trends of the coassembly at a constant temperature (below LCST), and therefore we do not take important changes in solubility of PNIPAm with temperature into consideration. We compare experimental and simulation data and analyze general trends of the behavior from the point of view of the used model. This approach allows us to interpret potential differences as a result of specific interactions between PNIPAm units and water and their changes upon the micellization and upon the incorporation of surfactant molecules into associates.

■

EXPERIMENTAL SECTION

Materials. Dodecyl- and carboxyl-terminated poly(N-isopropylacrylamide) (mPNIPAm, Scheme 1) was synthesized by RAFT

Scheme 1. Structure of mPNIPAm

polymerization using S-1-dodecyl-S′-(α,α′-dimethyl-α″-acetic acid)trithiocarbonate as a chain transfer agent. Characteristics of both mPNIPAm unimer and micelles are summarized in Table 1; details on

Table 1. Parameters of mPNIPAm Unimers and Micelles Obtained from SEC, LS, and SAXSa Mw,b kg mol−1 6.2

Mw/Mnc 1.2

R,d nm 7.7

RHe 7.8

Naggf 13.8

a

Micelle parameters were determined for aqueous 5 mg/mL solution in 0.1 mM NaOH (pH 8). bWeight-averaged molar mass of mPNIPAm unimer from SEC in THF. cDispersity index of mPNIPAm unimer from SEC in THF. dmPNIPAm micelle radius from SAXS (sphere form factor). emPNIPAm micelle hyd. f mPNIPAm micelle aggregation number from SAXS.

synthesis and characterization of mPNIPAm are given in our previous study.18 N-Dodecylpyridinium chloride (DPCl) was purchased from Sigma-Aldrich. 5-(N-Dodecanoyl)aminofluorescein (DAF) was purchased from Molecular Probes (Eugene, OR). In this study, 1 mg/mL mPNIPAm solutions in 0.01 M NaOH (pH 12.7) were used for all measurements expect for SAXS and ITC, B


Article

Macromolecules

■

RESULTS AND DISCUSSION Experimental Studies of the mPNIPAm/DPCl System. Earlier studies of the modified mPNIPAm in high pH aqueous media at ambient temperatures indicate that mPNIPAm alone forms the core−shell associates with relatively stretched PNIPAm blocks and with ionized −COO− groups preferentially localized at the shell periphery.17,18 The associates are stabilized in the solution by the shell of PNIPAm chains that are still reasonably soluble at 25 °C and by the strongly negative ζ-potential generated by −COO− groups at the end of PNIPAm chains. The addition of DPCl leads to structural changes which are the topic of our present study. The behavior is complicated, and the explanation of observed experimental trends in a broad range of DPCl-to-mPNIPAm ratios Z has to be based on results of several experimental methods and computer simulations. In the next part, we will present and elucidate the results of individual techniques step by step, but we have to make clear that the coherent description and explanation of the behavior will emerge only at the very end of this part. The study of the coassembly of mPNIPAm with DPCl was performed in a broad range of Z. We present experimental data in the whole Z range, but for the sake of smooth discussion, we focus more on low Z first, and later we explain gradual changes of the coassembling behavior in mixtures with excess of surfactant. We start our discussion with electrophoretic light scattering measurements of the ζ-potential because they provide very important information about the studied coassembly which serves as a guideline for further studies. Adding DPCl to the mPNIPAm micellar solution leads to the compensation of negative charge of mPNIPAm micelles by positive charge of surfactants (see Figure 1a). The gradual decrease of absolute

contribution of small ions to the overall effect cannot be precluded. The charge compensation is very efficient, which is demonstrated by the fact that the ζ-potential reaches zero close to the charge ratio Z = z+/z− = 1. As the dodecyl tails of the surfactant are strongly hydrophobic and identical with core-forming dodecyl groups of mPNIPAm, we assume that the surfactant tails solubilize at low Z < 1 almost exclusively in the cores of the self-assembled nanoparticles. Because the contour length of hydrophobic parts is the same, the surfactant tails can be easily accommodated in the cores of mPNIPAm nanoparticles with their charged headgroups localized in the core−shell interfacial region. It is obvious that the effective compensation of negative charges localized at the outermost periphery of original mPNIPAm micelles by the positive charge of surfactant chains entering in the inner part of associates requires non-negligible spatial relocation of charged groups and structural changes of associating chains. In analogy with the conformational behavior of water-soluble end-modified shell-forming chains (tagged by hydrophobic fluorophores) in aqueous solutions of amphiphilic micelles,22 we assume that the attractive electrostatic interaction of oppositely charged groups induces the collapse of some shell-forming PNIPAm chains, which enables the close approach of the carboxyl-decorated ends toward the core−shell interface. The outlined mechanism supposes that the entropic penalty due to the collapse of PNIPAm chains is smaller than that caused by the condensation of small and mobile ions in the core−shell region, which has been proven by simulations (see later). The collapse of chains increases the density of the inner PNIPAm shell which promotes the formation of intra- and interchain H-bonds, thereby lowering the hydrophilicity of the inner PNIPAm shell. Additional information about the binding and localization of surfactant headgroups in mPNIPAm micelles was obtained by fluorescence quenching measurements with N-dodecanoylaminofluorescein (DAF) which strongly binds to nonpolar cores of various self-assembled associates with its fluorescent headgroup located in the innermost part of the water-soluble shell (close to the core−shell interface).23 The fluorescence of DAF is quenched by DPCl headgroup24 and therefore the decrease of fluorescence emission and shortening of fluorescence lifetime reports on the close approach of DPCl headgroup to DAF headgroup. We followed the binding of DP+ ions to mPNIPAm micelles and their localization by measuring the time-resolved fluorescence emission of DAF and by interpreting the results on the basis of the micellar quenching model.19 Fluorescence emission decays, F(t), their fits to the micellar quenching model, and results of the fits are shown in the Supporting Information (Figures S1 and S2). The used model assumes that the micelle contains one fluorophore and several quenchers at relatively close distances from the fluorophore. The ensemble-average decay, F(t), can be described by a simple equation which contains only one quenching rate constant kq and the average number C of quenchers per micelle. The equation reads ÄÅ ÉÑ Å t Ñ F(t ) = F(0) expÅÅÅÅ− − C(1 − e−kqt )ÑÑÑÑ ÅÇ τ ÑÖ (1)

Figure 1. (a) ζ-Potential, (b) parameter C (eq 1), and (c) the cloud point temperature, Tcp, of the mPNIPAm/DPCl system as functions of the charge ratio Z.

values of the negative ζ-potential upon the stepwise addition of DPCl proves that the surfactant solubilizes in micelles (more precisely, it coassembles with mPNIPAm), and the negative charge of −COO− groups at the ends of PNIPAm chains of original micelles (without surfactant) is neutralized mainly by the positive charge of surfactant headgroups, even though the

where τ is the emission lifetime of the unquenched fluorophore and F(0) is the fluorescence intensity at t = 0. The measurements show that the fluorescence is strongly quenched upon addition of DPCl. The quenching effect increases with the amount of added surfactant. The parameter C is plotted as C


Article

Macromolecules a function of Z in Figure 1b. It is obvious that the number of quenchers in the core−shell interface increases with the amount of added surfactant. At high Z, it almost levels off and approaches the saturation value, although the growth is less steep than in the case of the ζ-potential, and the shape of the curve suggests that the plateau would be achieved for appreciably higher values than Z = 4. Significant increase of C for Z < 1 unambiguously proves that in the low Z region the aliphatic tails of the comicellized surfactant solubilize in dodecyl cores with their headgroups localized in the innermost part of the shell. Additional information necessary for the understanding of the coassembling mechanism and for interpretation of its trends was obtained by cloud point measurements. It was reported that the addition of cationic surfactants to PNIPAm aqueous solution increases LCST.25 The hydrated PNIPAm chain is basically incompatible with the aliphatic tail of the surfactant, but the dehydrated nucleation centers, which start forming at LCST, are fairly hydrophobic and interact favorably with aliphatic surfactant tails; i.e., the surfactant covers and stabilizes the partially dehydrated PNIPAm chains in the solution. As a consequence, the LCST of the mixture increases. However, in spite of the above observation, the cloud point temperature, Tcp, of the mPNIPAm/DPCl micelles decreases with increasing Z (see Figure 1c). Temperature dependences of scattering intensity are shown in Figure S3. This behavior indicates that Tcp of the mPNIPAm/DPCl system is affected by electrostatic interaction between −COO− groups of mPNIPAm with DP+ chains and at higher Z also by the repulsion between mPNIPAm/DPCl micelles. It was shown previously by Tcp vs pH dependence for neat mPNIPAm micelles that the ionization of the carboxyl end-group promotes the solubility of mPNIPAm.18 In the studied system, both effects influence Tcp, but the electrostatic effect dominates over the hydrophobic effect as it is also proven by the simulation study (see later). We can summarize that the LCST behavior clearly indicates that a number of −COO− groups are engaged in a strong (short-range) interaction with surfactant headgroups in mPNIPAm/DPCl coassembled particles, and their charge is effectively neutralized which supports the assumption on the collapse of a fraction of chains. As already mentioned, the density of inner shell increases upon the collapse of some PNIPAm chains, and because the high density of PNIPAm building units promotes the formation of H-bonds between them, the inner shell becomes more hydrophobic. Simultaneously, the outer shell dilutes, and its PNIPAm units remain solvated and stabilize the coassembled particles in the solution. The structure of the shell is then reminiscent of a “double-layer shell” of micelles with poly(methacrylic acid) shell-forming blocks like polystyrene-block-poly(methacrylic acid), PS−PMAA,26 in which the density profile of PMAA as a function of the distance from the core−shell interface (and also the degree of ionization) can be represented by sigmoidal curves in a broad pH range (except for very high pH 12−14). We assume that the “onion-like” structure of associates affects the scattering experiments. Before we discuss the scattering measurements, we want to point out that ITC measurements (Figure S4) indicate that up to Z ca. 5 no important heat effects occur. The titration of DPCl into mPNIPAm solution leads to a very small thermal response of ca. −0.5 kJ mol−1, which is much less than the demicellization enthalpy of DPCl in 0.01 M NaOH, ΔHdemic = −2.3 kJ mol−1. This suggests that the tails of DP+ ions are

resolubilized in dodecyl cores and later also in the fairly hydrophobic inner shell of mPNIPAm associates and experience similar interactions as in surfactant micelles above the cmc in the solution used for the titration. Only in mixtures with Z > 5, the addition of DPCl provokes the exothermic rearrangement of micelles with the maximum heat effect at Z ca. 25, corresponding to DPCl concentration of 12 mM, which is slightly lower than its cmc in 0.01 M NaOH. Figure 2 shows intensity-weighted distributions of hydrodynamic radii obtained by dynamic light scattering (DLS). The

Figure 2. DLS distributions of hydrodynamic radii for mPNIPAm/ DPCl aqueous solutions (mPNIPAm concentration, c = 1 mg/mL). Charge ratios Z are indicated above the individual curves.

distributions consist of a fast mode corresponding to diffusion of mPNIPAm/DPCl micelles and a slow mode (or two slow modes in the case of Z = 8) corresponding to diffusion of loose mPNIPAm/DPCl aggregates. The aggregates form due to restricted solubility of PNIPAm, which is not far from the LCST at ambient temperature. The existence of the large aggregates was confirmed also by SAXS and by computer simulations (see later). In the neat mPNIPAm system, the peak with maximum at ca. 8 nm corresponds to mPNIPAm micelles. The coassembly of mPNIPAm with DPCl leads to the increase of RH of mPNIPAm/DPCl micelles (the maximum shifts to 14 nm). It is noteworthy that the position of the maximum of the peak of micelles changes only negligibly for Z from 1 to 8. Figure 3 shows SAXS curves for the mPNIPAm/DPCl system at various Z ratios. While the scattering behavior for q > 10−1 nm−1 indicates the formation of spherical core/shell micelles, the power-law regime for q < 10−1 nm suggests the presence of larger aggregates, which was confirmed also by DLS (Figure 2) and by simulations (see later). Power-law exponents (see Table S1) are mostly larger than 3, indicating that at the length scale of ∼102 nm the aggregates are homogeneous and scattering occurs at their rough surface. While the micellar scattering was treated by the form factor for the homogeneous sphere surrounded by self-avoiding chains, the scattering from the large aggregates was fitted with the power-law term. The details of the model and data fitting are provided in the Supporting Information. The size parameters, i.e., the radius of the core, Rcore, the gyration radius of shell chains, Rg, and the micelle radius, Rmic, calculated as Rmic = Rcore + 2Rg assuming that the shell thickness is equal to 2Rg of the shell-forming chains, obtained by fitting the SAXS curves are depicted in Figure 4. The radius of micelles does not change much, but the size of the cores and the thickness of the shell undergo quite pronounced changes. For small Z < 1, the core radius, Rcore, slightly increases and levels off for 1 < Z < 2 with Rcore ca. 2 nm, then it increases D


Article

Macromolecules

undergoes non-negligible modification at Z > 1. At high Z, all dependences measured by different techniques in Figure 1 exhibit the saturation-like behavior. The analysis of light scattering and SAXS data indicates gradual changes in the structure of coassembled nanoparticles for Z > 1. The radius of the core increases, and the thickness of the shell shrinks. However, the ζ-potential levels off for Z ca. 1 and remains almost zero, which indicates efficient charge compensation and important nonelectrostatic stabilization of coassembled nanoparticles in the solution by hydrated parts of PNIPAm chains in systems with Z > 1. On the basis of our experimental results, we can propose the following coassembling scheme for Z > 1, which we will further test by computer simulations: As the size of the core is restricted (i) by the contour length of dodecyl groups of mPNIPAm and (ii) by strong incompatibility of charged surfactant headgroups and dodecyl tails, higher numbers of surfactants (appreciably higher than the number of core-forming blocks) cannot be accommodated in spatially restricted cores of original mPNIPAm micelles. Three scenarios come into account. The first scenario (based on a simplified model) does not take the specific role of hydrogen bonds in PNIPAm solutions into account. It assumes that the system is not kinetically frozen, and the replacement of some mPNIPAm chains in associates by surfactant chains and consequent fast re-equilibration of the associating system enable thus the formation of an appreciably higher number of associates with surfactant-rich cores and lower numbers of mPNIPAm chains. In such a case, a high surplus of surfactant can coassemble with mPNIPAm without forming a nonnegligible fraction of surfactant micelles in the solution. In the studied system, the above scheme is not very probable, but it can be easily studied by simulations, and the comparison of experimental and simulation data helps to identify the effects caused by specific interactions and to appraise the role of hydrogen bonds. The second (a more probable and our preferred) scenario reflects the well-recognized effect of hydrogen bonds on the behavior of the studied copolymer. PNIPAm is at ambient temperatures close to LCST, and its phase transition at elevated temperatures is a result of its massive dehydration connected with important redistribution of hydrogen bonds between PNIPAm units and water in favor of bonds between the pairs of polymer building units. The formation of H-bonds between different components of the mixture depends not only on temperature but also on the density of PNIPAm units. In analogy with different behavior of inner and periphery parts of PNIPAm stars,10 we suppose that high density of PNIPAm chains and insufficient numbers of water molecules in the inner parts of the star facilitate the formation of H-bonds between PNIPAm units and the dehydration of the inner part of the star. We assume that the addition of higher amounts of surfactants promotes the formation of a compact dehydrated (fairly hydrophobic) layer in the inner part of the PNIPAm shell around the original dodecyl core, which in turn enables the solubilization of surfactant dodecyl groups as a result of their favorable interaction with dehydrated PNIPAm units which causes, e.g., the observed increase of LCST in aqueous solution of linear PNIPAm chains.25 The third (supplementary) scenario can explain structural changes that occur at high surfactant-to-mPNIPAm ratios, Z. Assuming that not all PNIPAm chains are collapsed and not all carboxylate groups are engaged in electrostatic interaction with heads of the core-embedded surfactant, some surfactant ions

Figure 3. SAXS curves for mPNIPAm/DPCl aqueous solutions (mPNIPAm concentration, c = 5 mg/mL). Charge ratios Z are indicated above the individual curves. Intensities of the data are incrementally shifted by a multiplicative factor 10 for better readability; data for the mPNIPAm solution (Z = 0) are directly at scale.

Figure 4. Gyration radius of the shell chain, Rg (curve 1), the radius of the core, Rcore (curve 2), and the micelle radius Rmic = Rcore + 2Rg (curve 3) for mPNIPAm/DPCl aqueous solutions (mPNIPAm concentration, c = 5 mg/mL) as functions of charge ratio Z.

again, and for Z > 4 Rcore reaches a relatively large value of ca. 6 nm and almost levels off again. The thickness of the shell slightly increases with the addition of the surfactant, but then it drops in the Z range 2−4 and later remains constant. The changes of structural parameters are consistent with the hypothesis that at Z > 2 the inner PNIPAm shell collapses and forms a fairly dense and considerably hydrophobic layer around the original dodecyl core. In analogy to the already accepted mechanism that explains the observed increase of LCST of linear PNIPAm upon the addition of a cationic surfactant,25 we assume that the dodecyl tails of the added surfactant are appreciably more compatible with the dehydrated parts of PNIPAm chains than with water and solubilize in the inner shell layer. The parts of dehydrated PNIPAm chains can consequently slightly intermix also with dodecyl groups of mPNIPAm, and the compact central parts of mPNIPAm micelles are “perceived” as dense cores in scattering studies. At the end of this section, we would like to summarize the features of the observed behavior with accent to the high Z region. Experimental data show that increasing amounts of surfactants are readily incorporated into coassemblies at higher Z, but it is obvious that the coassembling mechanism E


Article

Macromolecules can associate in the shell periphery at the ends of stretched PNIPAm chains in surfactant-rich mixtures even below the cmc of the surfactant.27 As a result, some structural changes and the formation of mPNIPAm core−shell micelles decorated at the shell periphery by a surfactant associate cannot be precluded. However, the number of negatively charged groups per one mPNIPAm micelle is relatively low, and all experimental data indicate that the role of electrostatics is minor as compared with hydrophobic effects. Because our simulations were performed only in a relatively low Z range, we did not investigate the third scenario in detail. Model and Strategy of Coarse-Grained Simulations. The experimental study showed that the observed coassembling behavior of modified poly(N-isopropylacrylamide), mPNIPAm, with surfactants is a result of intricate interplay of a number of factors. The mPNIPAm/DPCl coassembly depends not only on solvophilic/solvophobic effects and electrostatic interactions but also on different specific interactions, particularly on hydrogen bonds between the components and on their changes upon the association. Hydrogen bonds and solvation effects can be, in principle, addressed and treated by coarse-grained simulations, but we are of the opinion that their successful emulation often leads to a wishful (not fully physically justified) setting and variation of interaction parameters. Therefore, we adopted a different strategy of our computer study. We do not attempt to reproduce the observed trends at any cost, but we will analyze clear features of the behavior caused by nonelectrostatic coarse-grained interactions and long-range electrostatic interactions first. We will use the conclusions of our analysis for identification of general trends of the studied coassembly and then we will interpret potential differences between the experimental and computer-emulated behaviors as results of specific interactions (hydrogen bonds and their redistribution due to addition of surfactants). As already stated, we study the behavior of the system at a constant temperature, and therefore we do not have to consider important changes of PNIPAm solubility with temperature. The computer modeling and parameter setting are based on a series of our recent DPD studies.28−32 The most important details on DPD can be found in the original literature33−39 and are explained also in the Supporting Information. We model the modified mPNIPAm as a flexible string of two types of DPD beads kept together by harmonic springs. The beads are arranged in two blocks: the chain starts with three hydrophobic beads A emulating the dodecyl group and continues with 30 hydrophilic beads B emulating a relatively long PNIPAm chain. The last bead B bears one negative elementary charge which corresponds to the presence of one carboxyl group attached at the very end of the PNIPAm chain which is dissociated (ionized) in alkaline solutions. The numbers of beads of both types were set according to relative lengths of hydrophobic and hydrophilic blocks in the sample studied experimentally. The employed model is shown in Scheme 2, and the values of all interaction parameters used in simulations are summarized in Table 2. The parameter describing the interaction of beads A with solvent S is strongly repulsive (hydrophobic), aAS = 48.5. The B−S interaction, aBS = 27, reflects marginal solubility of PNIPAm in aqueous solutions slightly below LCST;1 i.e., it roughly corresponds to the ϑ-solvent conditions (aij = 26.64 emulates the θ-state (χ = 1/2)35). Both parameters were optimized to get the experimentally estimated association

Scheme 2. Schematic Representation of the Studied Systema

a

Red beads represent the dodecyl terminal group of mPNIPAm, green beads the PNIPAm units, dark blue beads the carboxylate terminal group of mPNIPAm, and yellow and dark gray respectively the dodecyl group and the headgroup of the surfactant. The scheme shows how the chains coassemble and self-organize into a core−shell micelle, the sector of which is depicted on the right-hand side of the figure.

Table 2. Repulsion Parameters, aij, between Components of the Studied Systema aij A B, B− H+ solvent, CI

A

B, B

25

40 25

−

H+

solvent, CI

25; 30; 50 25 25

48.5 27 25 25

A, B, B−, H+, and CI stand for dodecyl groups, PNIPAm units, terminal carboxylate groups, and surfactant headgroups for counterions respectively. a

number As of mPNIPAm micelles without added surfactant. With regard to the interactions between other components, we assume that the aliphatic chain of the surfactant behaves as dodecyl in the polymer and that the counterions are compatible with the PNIPAm block and incompatible with aliphatic blocks of the copolymer and the surfactant. The surfactant headgroup is based on a hydrophobic group, but it bears one positive elementary electric charge, e. Its solubility is a result of electrostatic interactions with the water-dispersed counterions, which are explicitly taken into account in our DPD simulations. The headgroup is chemically different from the surfactant aliphatic chain, and therefore we performed the simulations (i) for the headgroup moderately incompatible with the aliphatic tail (a+AH = 30), but for comparison, we did two additional series of simulations: (ii) for the highly incompatible (a+AH= 50) and (iii) for the fully compatible headgroup (a+AH = 25). The differences will be discussed in pertinent parts and mainly in the Supporting Information. The simulations were performed for the self-assembling system of 123 A3B29B− polymer chains in a simulation box of the size 303 with periodic boundary conditions in all 3D (the length unit is defined as a cutoff radius of DPD bead), which is always electroneutral thanks to the presence of appropriate numbers of counterions and added salt ions. As already mentioned, solvent molecules are treated explicitly in DPD simulations. The volume fraction of the polymer is 5 vol %. The added surfactant molecules are modeled as relatively short flexible strings of four DPD beads: three beads A and one positively charged bead H+, the interactions of which have already been discussed. On the basis of mutual relation between DPD interaction parameters and the Flory−Huggins interaction parameter χ,35 we assume that each polymer bead corresponds roughly to one Kuhn segment. The number of added F


Article

Macromolecules

Figure 5. Typical snapshots of simulation with varying number of surfactants: (a) without surfactant chains, (b) 60 surfactant chains (0.296 vol %), (c) 123 surfactant chains (0.607 vol %), and (d) 430 surfactant chains (2.12 vol %). Upper row shows all polymer and surfactant beads, while lower row does not show B block (that is, it shows associate core). Red beads represent A block of PNIPAM, green beads B block, blue beads B− beads, yellow beads A block of surfactant, and gray beads H+ beads.

Figure 6. (a) Number distribution functions of associates, Fn(Asn) (red curves), weight distribution functions, Fw(Asn) (green curves), and zaverage distribution functions, Fz(Asn) (blue curves), as functions of the net association numbers, Asn, for system without added A3H+. (b) Radial density profiles of A beads (red curve, left axis), B beads (green curve, left axis), B− beads (blue curve, right axis), and counterions (violet curve, right axis) for aggregation number Asn = 30. (inset) Radial charge density profile: total charge (full cyan curve), charged end-groups of mPNIPAm (broken green curve), and counterions (dotted violet curve).

surfactant chains varies from 0 to 430; i.e., their volume fraction varies from 0 to 2.1 vol %. The simulated coarsegrained chains are shorter than the experimentally studied chains as it is common in computer simulations of multichain systems. The values of unfavorable nonzero interaction parameters (χ > 0) are larger than those estimated by appropriate experimental measurements because they were rescaled (similarly as the parameters used in most simulation studies) using the relation Nsimχsim= Nexpχexp, where Nsim and χsim are the length and interaction parameter of model chains and the symbols with subscript “exp” are the corresponding experimental values.40 The solvent beads correspond roughly to three water molecules, and the co- and counterion beads correspond to the hydrated small ions. The size of all types of beads is constant in our simulations. We used the simulation program DL-MESO41 with implemented explicit electrostatics.42 All other relevant pieces of information about our simulations can be found in the Supporting Information. Results and Discussion of the Simulation Study. The experimental study indicates that mPNIPAm alone forms the core−shell micelles in aqueous media with relatively small dodecyl cores. Therefore, we performed the simulations for the neat copolymer system (123 mPNIPAM chains in the simulation box) without surfactant chains first. In further simulations, we added increasing amounts of surfactant chains into the simulation box. For comparison, we studied the surfactants with compatible and incompatible headgroups.

In Figure 5 we present four snapshots of the simulation box which show typical associates formed in aqueous mixtures of A3B29B− chains with increasing amounts of added surfactant chains A3H+ (upper row, Figure 5a−d) and corresponding core-forming blocks (lower row, Figure 5a−d). A close visual inspection of individual figures is interesting and reveals important details of the behavior. Figure 5a depicts the pure mPNIPAm system without added surfactant chains. The snapshots show that the neat mPNIPAm system forms distinct core−shell associates. In the lower part of Figure 5a we see several well-separated cores of mPNIPAm micelles depicted by yellow beads A. The comparison of upper and lower of Figure 5a reveals that some single mPNIPAm chains (i.e., also their A3 chains) are dispersed in PNIPAm shells (depicted by green beads B) and that the shells of some core−shell associates at a given concentration interpenetrate, which results in formation of fluctuating (temporary) associates of micelles. In a system with 60 added surfactant molecules (the ratio of positive-tonegative charges, Z = 0.5; the lower part of Figure 5b), we see the cores formed of A beads from both mPNIPAm (yellow) and surfactant (gray) with a number of surfactant headgroups (red beads H+) preferentially distributed on their surface. Analogously to the pure mPNIPAm system, some single mPNIPAm chains are dispersed both in bulk solvent phase and in micellar shells. In this system, an important fraction of negatively charged end-groups B− (blue) return back to the positively charged cores, which assumes that some B29B− G


Article

Macromolecules

Figure 7. Number distribution functions of associates, Fn(As) (red curves), weight distribution functions, Fw(As) (green curves), and z-average distribution functions, Fz(As) (blue curves), as a function of the total association numbers, Ast (i) (left column), and as functions of the net association numbers, Asn (right column), (a, b) with 123 added A3H+and (c, d) with 430 added A3H+.

number; this is why the weight and z fractions of associates with large As are always higher than corresponding number fractions. In the studied system, the situation is slightly more complicated because the weight of associates with coassembled surfactants includes not only the weight of associated mPNIPAm chains but also that of surfactants. The weight of surfactant chains is more than 10 times smaller than that of mPNIPAm. The weight (mass) average molar masses, Mw measured by static light scattering and the z-based average radii of gyration, RG and hydrodynamic radii, RH depend mainly on the number of associated mPNIPAm chains, but at higher Z, they are affected by coassembled surfactant molecules. When we classify the associates formed during the simulation run, we evaluate independently the numbers of self-assembled A3B29B− chains and the numbers of coassembled surfactants A3H+. Therefore, we define (i) the net association numbers, Asn = Np, based on the numbers of A3B29B− only and (ii) the total association numbers, Ast = Np + Ns, which include also the numbers of coassembled surfactant molecules and are higher than the former ones. In the inset of Figure 6b, we present the charge distribution inside the associates and in their immediate vicinity. The broken green curve shows the distribution of negatively charged mPNIPAm end-groups. This curve is basically a mirror image of the broken blue curve in the mainframe (b). The dotted violet curve shows the distribution of counterions, and the full cyan curve depicts the total charge distribution. The total charge drops to zero at r ca. 8, but it is still negative at the shell periphery at r ca. 5−6. Figure 7 consists of two columns of frames. The left-handside column (Figures 7a and 7c) shows Fn(Ast) as red curves, Fw(Ast) as green curves, and Fz(Ast) as blue curves for (a) systems with 123 and (c) with 430 added A3H+ surfactants. The corresponding system without added A3H+ is shown in Figure 6a; the distribution functions for more systems are shown in Figure S5. The shapes of distributions plotted as functions of Ast change only a little. They slightly broaden with increasing amount of added surfactant chains, but the positions of maxima do not change much. The right-hand-side column

chains either collapse or recoil back toward the core. On the basis of a close analogy (concerning the interplay of competing forces) with the conformational behavior observed in our earlier Monte Carlo studies of hydrophobically modified polyelectrolyte shell-forming chains,43 we assume that the collapse is more probable than the back-loop of B29B− chains. The addition of increasing amounts of the surfactant is accompanied by progressive incorporation of surfactant chains into micellar cores. The size of cores increases, and their surface becomes appreciably charged. The number of cores gradually grows, which in a system with constant number of A3B29B− chains means that the average number of associated mPNIPAm chains in one associate decreases. Nevertheless, the size of cores increases because they contain elevated numbers of surfactant chains. In all cases, the PNIPAm shells overlap and the system forms a fraction of micellar aggregates. The inspection of a number of snapshots (not shown) indicates that the aggregates are only loosely interconnected and that the system of associating chains is quite mobile (there exists an exchange of chains between micelles and quite mobile formation/decomposition of temporary micellar aggregates); i.e., we can conclude that the system of core−shell micelles and micellar clusters strongly fluctuates. In systems with Z = 1.0 and 3.5 (i.e., with 123 and 430 A3H+ chains), we see that a fraction of free surfactants in bulk slowly increases. In Figures 6 and 7, we present the results of simulations in a more quantitative way. We show the ensemble-average number distribution functions of associates, Fn(As) weight (or mass) distribution functions, Fw(As), and the z-average distribution functions, Fz(As). The former function is based on the number fractions of chains with given As, and the latter distributions depict either the weight fractions or the z fractions. The weight-average and z-average characteristics are commonly measured by various scattering techniques, and Fw(As) and Fz(As) are therefore more interesting for experimentalists than Fn(As). The weight fraction of a given associate is generally proportional to the product of its number fraction and its association number, and the z fraction is proportional to the product of its number fraction and the square of its association H


Article

Macromolecules (Figures 7b and 7d) shows the corresponding Fn(Asn), Fw(Asn), and Fz(Asn). They shift significantly to lower Asn with increasing amount of surfactant chains. When we compare both columns (in Figure 7 and Figure S5), we immediately observe that the number of associated mPNIPAm chains decreases with increasing amount of surfactant chains in the simulation box, but the surfactant chains are more and more incorporated in cores of associates. The dodecyl surfactant tails replace the dodecyl group of mPNIPAm. Therefore, the total association number, Ast, does not almost change, and the distributions of species with different Ast, particularly the positions of their maxima, do not almost shift. With respect to the fact that the changes of Asn report on the effect of surfactant on the mPNIPAm assembly, we will discuss the right-hand-side column in more detail. The observed trend is basically understandable: The cores formed by short dodecyl groups are relatively small. The increase in the core size is strongly restricted sterically because the dodecyl groups from the copolymer and from the surfactant are short and have to reach at the core−shell interface. The former ones are covalently connected with the shell-forming PNIPAm blocks, and the latter contain the electrically charged headgroup which prefers the location at the core−shell interface. The surfactant chains cannot fill in the central part of the core and cannot provoke the core expansion, which the neutral hydrophobic chains could do. Therefore, the incorporation of increasing amounts of surfactant molecules in dodecyl cores assumes the increase in the number of core−shell associates, which, in a system with a constant number of mPNIPAm chains, requires a decrease of the net association numbers Asn of mPNIPAm chains It should be pointed out that the simulation follows the already mentioned scenario based on a simple model system without complicating effects, such as the effect of hydrogen bonds. Simulation results for systems containing surfactants with more and less compatible headgroup are shown in the Supporting Information (Figure S7). The distributions for more compatible headgroups are broader and those for less compatible headgroups are slightly narrower than those presented in Figure 7 and more symmetrical, but the basic trends are the same as those already discussed. Radial density profiles, RDPi(r), of components enable detailed discussion of the structure of associates. Figure 8 shows the ensemble-average radial density profiles of individual components of the mixture RDPi(r) as functions of the distance r from the gravity center of the associate with Asn = 40 in four systems differing in the charge ratio Z, i.e., in the number of added surfactant chains. We present RDPi(r) for Z = 0.5, 1, and 2 (60, 123, and 246 surfactant molecules; note that the accurate value of Z for 60 surfactants is 0.49). The density profile of the associate with Asn = 30 in a pure mPNIPAm system (Z = 0) is shown in Figure 6b. The shapes of A and B profiles show without any doubts that mPNIPAm forms the multimolecular micelle-like core−shell particles with well-segregated core-forming and shell-forming blocks. The overlap of A and B density profiles around r = 2 suggests some intermixing of blocks in the core−shell region, but, as we have shown in our earlier papers,30 the apparent overlap is augmented by angular averaging of densities in associates, the size of which fluctuates and deviates from spherical symmetry. We have evaluated the main components of the gyration tensor of associates of all sizes ga, gb, and gc formed under given conditions and of their cores (ga)C, (gb)C, and

Figure 8. Radial density profiles for systems with A beads slightly incompatible with surfactant head a+AH = 30 and for aggregation number Asn = 40 for (a) system with 60 A3H+surfactant, Np = 26.4 and Ns = 13.6, (b) system with 123 A3H+surfactant, Np = 20.2 and Ns = 19.8, and (c) system with 246 A3H+surfactant, Np = 14.6 and Ns = 24.4. Left-hand axis is for A beads from mPNIPAm (red curves), A beads from A3H+ (ochre curves), B beads (green curve), and for H+ beads (black curve); right-hand axis is for B− beads (blue curve), positively charged counterions (violet curve), and negatively charged counterions (cyan curve). (insets) Radial charge density profiles: total charge (full cyan curves), charged end-groups of the surfactant and mPNIPAm (broken green curves), counterions (dotted violet curves).

(gc)C. They are shown in Figure S6. The ratio of values for the ensemble-average associate with As = 40 and Z = 0 is (i) 1.00:1.10:1.20 and 1.00:1.17:1.39 for Z = 2. The ratios of gyration components of corresponding cores are (i) 1.00:1.33:1.66 and (ii) 1.00:1.29:1.65. It is evident that the coassembled particles are on average fairly spherical. To give the reader better idea, the ratio of gyration components of the ellipsoid representing an ideal (interpenetrating) high-molarmass chain is 1.0:1.6:3.5.44 Even though the ensemble-average shapes do not deviate much from the spherical symmetry, the inspection of a number of simulation snapshots reveals (not shown) that instantaneous shapes of some associates appreciably differ from spherical. It is interesting that the charged end-beads B− in the pure mPNIPAm micelles (Figure 6b) are distributed throughout the whole shell; i.e., the single charge at the ends of the shellforming blocks does not cause the stretching of the majority of B blocks. Nevertheless, if we take into account the average spherical symmetry of micelles (i.e., the increase of the volume of spherical layers of the thickness Δr with r2 which are used I


Article

Macromolecules

compensated at short distances by counterions that partially concentrate in the shell and particularly at the core−shell interface. In all surfactant-containing systems, the concentration of the charge at the shell periphery decreases considerably, which explains the negligible ζ-potential of nanoparticles coassembled in systems with Z > 1. The DPD simulations with explicit electrostatics enable a straightforward evaluation of the electrostatic potential in a given place. Therefore, we evaluated the radial (angularly averaged) dependences of the electrostatic potential ϕ(r) of the associates similarly as in the case of RDPs of components: After the identification of the associate with a given association number AS and after the estimation of its center of gravity (x0, y0, z0) in a certain snapshot of the simulation box, the potential was evaluated for a sufficient number of uniformly distributed points on the spherical surface with radius r and the center in (x0, y0, z0), and the values were angularly averaged. This was performed for a number of r values. The obtained values ϕ(r) for associates with given AS and a set of different r were then averaged over a large number of snapshots in the equilibrated part of the simulation trajectory where the associates with this AS appeared. The radial dependences of ϕ(r) are shown in Figure 9. For the system without added surfactant, the potential is non-

for normalization of bead densities) and compare the decreasing density of segments B in the r-region between 3 and 8 with a shallow maximum of B− density at r ca. 5.5, it is clear that a non-negligible fraction of B chains are radially stretched. The charge of B− beads is partially compensated at short distances by small counterions which are compatible with PNIPAm chains. Therefore, they easily penetrate into the shell, and their density across the shell is almost uniform. Because some counterions move also in bulk solvent in the vicinity of mPNIPAm associates, their density in the shell is lower than that of B− beads, which explains the negative ζ-potential observed by electrophoretic light scattering measurements. Figure 8a shows RDFi(r) for the system with Z = 0.5. It is obvious that the basic core−shell structure does not change. Some A3B29B− chains in cores are replaced with surfactants A3H+, but the shapes of A beads density (from both mPNIPAm and surfactant) and B density are qualitatively the same as in Figure 6b. As expected, the H+ beads (surfactant headgroups) concentrate at the core−shell interface. The most interesting is the observation that the B−density profile changes significantly. The maximum density of B− beads shifts to the core−shell interfacial region and simultaneously is very pronounced as compared with the previous case. The density of negative Cl− ions (counterions of the surfactant) is fairly low in the whole shell region. This indicates that the positive charge of surfactant headgroups is non-negligibly compensated by the negative charge of the B− beads at the ends of mPNIPAm blocks. Nevertheless, the change of the B− profile requires that an important fraction of the shell-forming chains collapse which (in the case of entirely flexible chains) seems to be less unfavorable from the entropy point of view than the loss of translational entropy of small ions. When the number of added surfactants and the overall concentration of negative counterions increase, some negative counterions also concentrate close to the core−shell interface (see Figures 8b and 8c). To summarize the most important observations concerning the chain conformations, the DPD study shows that the density profile of the charged end-groups significantly changes upon addition of the surfactant, while the profile of all the shell-forming chains remains unchanged. This apparent paradox can be easily explained on the basis of data that we obtained some time ago by Monte Carlo simulations on a similar system.43 This study aimed at the self-assembled core− shell micelles, in which, analogously to the presently studied system, the ends of the shell-forming blocks were strongly attracted by the blocks at the core−shell interface, unambiguously proving that some shell-forming chains collapse in the vicinity of the core−shell interface but other chains are expelled from this region due to excluded volume effect and become slightly more stretched (mainly close to the interface). As a result, the density profile of the shell (formed by a high number of beads) does not almost change, but the distribution of chain ends, which reflects the increase of the number of ends close to the core−shell interface, appreciably changes. To give an overview on the behavior of charged species, in the insets of Figure 8 we depict the radial charge distributions inside the associates and in their immediate vicinity. The broken green curve shows the sum of charges at the surfactant headgroups and at the charged mPNIPAm headgroups and the dotted violet curve that on counterions. The full cyan curve shows the total charge. It is obvious the core−shell interface is strongly positively overcharged, and the charge is only partially

Figure 9. Radial dependences of the angularly averaged electrostatic potentials, ϕ(r), for associates without (black curve for AS = 30) and with added surfactant (AS = 40) for Z = 0.49 (full red curve), Z = 1.0 (dotted green curve), and Z = 2.0 (broken blue curve). (inset) Dependences of the electrostatic potential at the shell periphery: for r = 6.0 (full red curve), r = 6.5 (dotted green curve), and r = 7.0 (broken blue curve).

negligibly negative at the shell periphery and decreases in the direction to the core−shell interface. Because the charges are distributed in the whole shell, the slope of the decrease does not change much. The C12 core does not contain any charges and the potential is constant there, in agreement with the electrostatic theory. In systems with added surfactant, the shape of curves is quite reminiscent of that for the conductive sphere with the charge homogeneously distributed at its surface, except that the slope changes smoothly. It reflects the fact that the core−shell interface is strongly positively overcharged, the concentration of negative end-groups in the outer shell is relatively mild, the total charge is significantly screened by counterions, and the inner C12 core is essentially neutral. The dependences of the potential ϕ(r) at the shell periphery (for r = 6.0, 6.5, and 7.0) on Z are shown in the inset. We can conclude that its shape qualitatively agrees with the experimentally measured dependence of the ζ-potential on Z (Figure 1a). J


Article

Macromolecules At the end of the simulation part, we summarize the most important results and compare data obtained for systems differing in compatibility of the surfactant headgroup H+ with the core-forming beads A. The simulations were conducted for three values of incompatibility parameter aAH (25, 30, and 50), but the results for different aAH were qualitatively similar. Therefore, we show here only the results for aAH = 30; the curves for aAH = 25 and aAH = 50 are shown in Figures S9− S13. Figure 10 shows the dependence of z-average radii of gyration of the associates, ⟨RG⟩z/⟨RG⟩z,0 (curve 1), and of the

Figure 11. Average numbers of surfactant molecules, ⟨Ns⟩, as functions of the number of mPNIPAm chains, ⟨Np⟩, for different amounts of added surfactant (aAH = 30).

linear; for higher Z, the initial slope (which corresponds to the loose oligomers) is quite steep, but for Np > 10, the increase of ⟨Ns⟩ vs Np, which corresponds to core−shell associates, slows down. Figure 12 shows the dependence of the ensemble weightaverage molar mass of associates, ⟨M⟩w, vs Z. ⟨M⟩w reflects Figure 10. Normalized z-average radii of gyration of the whole associates, ⟨RG,⟩z/⟨RG,⟩z,0 (curve 1), and of the cores of the associates, ⟨RG,c⟩z/⟨RG,c⟩z,0 (curve 2), for associates with Ast > 10, as functions of Z (aAH = 30).

cores of the associates, ⟨RG,c⟩z/⟨RG,c⟩z,0 (curve 2), normalized by their values for Z = 0. While ⟨RG⟩z/⟨RG⟩z,0 decreases with increasing Z, which is mainly due to the already discussed decreasing dependence of average association number on Z, ⟨RG,c⟩z/⟨RG,c⟩z,0 increases in the region of low Z, and with the further increase of Z (for Z > 1), the size of the core remains constant. This indicates that some surfactant chains can easily incorporate into the cores of the micelles formed by a constant number of mPNIPAm chains with their headgroups localized in the innermost part of the PNIPAm shell close to the core− shell interface. Figures S8 and S9 show the same dependences for more values of the interaction parameter aAH. As already stated, the size of the insoluble core is a very important factor that controls the coassembly behavior. We see that the simulations based on a simple model that does not take specific interactions into account predict a non-negligible increase of the core radius. The plots are consistent with data presented in previous figures which show that some surfactant chains replace dodecyl groups of mPNIPAm chains in cores (decreasing the association number of copolymer chains) and that the number (concentration) of coassembled particles consequently increases with increasing Z. The comparison with experimental data and with results of simulations based on a more complex model will be shown in the part “The Comparison of Experimental and Simulation Data”. To get information about the distribution of surfactant molecules among associates differing in the association number of mPNIPAM chains, Np, in systems with increasing numbers of added surfactants, we plot average numbers of surfactant molecules, ⟨Ns⟩, vs Np in Figure 11 (and in Figure S10 more values of the interaction parameter aAH). In all cases, ⟨Ns⟩ increases with increasing Np according to intuitive expectation. In systems with low numbers of added surfactant molecules up to 123 (that is, up to Z = 1.0), the dependences are almost

Figure 12. Ensemble weight-average molar mass of associates, ⟨M⟩w, vs Z for associates with Ast > 10 and aAH = 30.

both the numbers and masses (weights) of coassembled particles. In the region of low Z, the values of ⟨M⟩w increase because the surfactant chains are incorporated into A cores, the size of which slightly increases (see Figure 5). Later the decrease in the number Asn = Np of associated mPNIPAm chains (with ca. 10 times higher mass than that of the surfactant) dominates the behavior, and ⟨M⟩ w values appreciably decrease with Z. It is noteworthy that for aAH = 50 (see Figure S11) the stronger incompatibility of the headgroups with A beads hinders the interpenetration, and no initial increase in ⟨M⟩w is observed. We feel that the methodology of evaluation of ⟨M⟩w values requires a short explanatory comment. The classification of temporary associates formed during the simulation run is based on a simple criterion which monitors a close approach of insoluble beads A from different mPNIPAM and surfactant chains. This means that we can easily and unambiguously discern the cores of associates and calculate the number of A3B29B− chains and the number of coassembled surfactants A3H+ chains which belong to individual cores, but we do not discern micellar clusters with interpenetrated B chains, which significantly affect the experimental scattering data. As is obvious from simulation snapshots, the PNIPAM blocks partially interpenetrate (see Figure 5). At Z > 1, the formation of micellar associates (clusters) could be reinforced by electrostatic interactions of free A3H+ chains with charged B− K


Article

Macromolecules groups at the ends of stretched ends of B29B− blocks. In the experimental mPNIPAM system, the formation of micellar associates can also be promoted by a well-known tendency of PNIPAM to form hydrogen bonds, which as explained in the part “Model and strategy of coarse-grained simulations”, we do not take into account. We are of the opinion that the above comment explains why we can reasonably reproduce the experimental behavior at the semiquantitative level for low Z and why the experimentally observed and simulated behaviors differ for large values of Z. Figure 13 summarizes the coassembling behavior in terms of ensemble average numbers of self-assembled chains of different

the radii of the core measured by SAXS and calculated by DPD (see Figure 14). It is obvious that the simulations reproduce

Figure 14. Normalized z-average radii of gyration of the core of associates, ⟨RG,c⟩z/⟨RG,c⟩z,0, as a function of Z (where ⟨RG,c⟩z,0 stands for the value for Z = 0) and aAH = 30 (red curve, associates with Ast > 10) and experimental data (green curve). The blue point corresponds to the simulation of the hypothetic triblock copolymer A3B*10B19B− described in the Supporting Information.

the experimental behavior at low Z ≤ 2 fairly well. They predict the initial increase of the core size for Z ≤ 0.5 and their leveling-off for 0.5 < Z ≤ 2. Nevertheless, the experimental values at Z > 2 increase again, which is not reproduced by the simulation. This discrepancy is the first clear result of specific interactions. As it was already explained in the part “Experimental Results and Their Discussion”, in analogy with the behavior of PNIPAm stars10 we assume that the inner part of the PNIPAm shell dehydrates earlier than the periphery and collapses upon addition of increasing amounts of surfactant chains. The PNIPAm units form intra- and interchain hydrogen bonds. Consequently, the scattering from the core covered by a dense part of the collapsed shell increases, which affects data analysis. The formation of hydrogen bonds in the inner part of associates and the increase of their rigidity causes a certain kinetic freezing of micelles and prevents the decrease of association numbers of associates containing high fractions of solubilized chains predicted by simulation. The decrease of the association number is further restricted because the dehydrated (more hydrophobic) PNIPAm domains can solubilize the dodecyl tails of surfactants in the layer around the original dodecyl core. This, we believe, results in the experimentally observed increase of the core size for Z > 2 and to the constant number of associated mPNIPAm chains in associates differing in the number of coassembled surfactant chains. In the Supporting Information, we show that the coassembling behavior at higher Z can be qualitatively emulated by DPD simulations with a slight increase of mutual attractive interaction between the beads of the inner part of the PNIPAm block and by a slight decrease of their solubility upon addition of larger amounts of the surfactant. As an example, we show the radial density profile of the associates in the system, where we selected one-third of the B block as the inner part to be collapsed upon addition of larger amount of the surfactant and changed the interaction parameters only by ±3. The corresponding density profiles are plotted in Figure S13. It is obvious that the density of inner B beads increases, and their distribution shifts toward the core which emulates the formation of a denser layer of PNIPAm around the dodecyl core. As we do not like the artificial playing with interaction parameters, we did not try to optimize the parameters and evaluate the size characteristics. The purpose of the auxiliary

Figure 13. Average numbers of self-assembled A3B29B− and A3H+ chains ⟨Np⟩ (curve 1) and ⟨Ns⟩ (curve 2) as functions of Z for associates with Ast > 10 (aAH = 30).

types, depicting separately the numbers of A3B29B− and A3H+ chains as functions of Z. As already mentioned, the numbers of A3B29B− chains pass maxima at Z = 0.5 and the numbers of A3H+ chains monotonously grow with Z. The sum of coassembled A3B29B− and A3H+ chains steeply grows in the region Z ∈ ⟨0, 1⟩, and then it almost levels off. From the comparison of curves for different aAH (see Figure S12), it is obvious that a hindered penetration of surfactant headgroups H+ into A core (emulated by increasing values of aAH) restricts the association process. This suggests that the limited length of the core-forming blocks (A3 blocks from the copolymer and surfactant which both have to reach at the core−shell interface) plays an important role in the stop-growth mechanism controlling the coassembling process. Comparison of Experimental and Simulation Data. The results presented in the preceding parts show that the coarse-grained simulation studies can emulate and elucidate a number of experimentally observed facts despite the fact that they are based on a simplified model that does not take into account the changes in the solubility of PNIPAm at constant temperature caused by the surfactant-induced redistribution of hydrogen bonds between the pairs of PNIPAm units and between PNIPAm and water pairs. They clearly indicate that the interplay of the short-range hydrophobic/hydrophilic interactions and long-range of electrostatic interactions qualitatively predicts and explains the formation of core− shell associates in the neat mPNIPAm system and the incorporation of cationic surfactants in the inner part of associates. Following the original strategy, it is interesting to analyze the quantitative discrepancies between the experimentally observed and simulation predicted trends from the point of view of specific interactions. Because the size of the core was identified as the most important parameter which controls and restricts the coassembly in the studied system, it is interesting to compare L


Macromolecules

■

study presented in the Supporting Information was to show that results of simulation with a physically sound qualitative modification of interaction parameters reflecting the changes in hydrogen bonding support the interpretation of experimental data.

Article

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.macromol.8b01161. Figures S1−S13; Tables S1 and S2 (PDF)

■

CONCLUSIONS We studied the coassembly of poly(N-isopropylacrylamide) with dodecyl and carboxylate terminal groups (mPNIPAm) with N-dodecylpyridinium chloride (DPCl) in alkaline aqueous solutions using a combination of experimental techniques (light scattering, SAXS, ITC, and fluorometry) and coarse-grained DPD simulations. Pure mPNIPAm formes micelles with the core of dodecyl terminal groups (Scheme 3a). Both ζ-potential and fluorescence measurements (using

■

AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected] (Z.L.). *E-mail: [email protected] (K.P.). *E-mail: [email protected] (M.S.). ORCID

Karel Š indelka: 0000-0003-3925-924X Mariusz Uchman: 0000-0002-2564-1985 Stergios Pispas: 0000-0002-5347-7430 Karel Procházka: 0000-0003-2144-5378 Miroslav Š těpánek: 0000-0002-7636-7234

Scheme 3. Structure of mPNIPAm and mPNIPAm/DPCl Micelles

Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS This work has been supported by the Ministry of Education, Youth and Sports of the Czech Republic (Operational Programme Research, Development and Education: “Excellent Research Teams”, Project No. CZ.02.1.01/0.0/0.0/15_003/ 0000417-CUCAM), by the Charles University Research Centre (Programme No. UNCE/SCI/014), and by the Czech Science Foundation (Grants 16-12291S and 1700289Y). The authors thank the European Synchrotron Radiation Facility (ESRF), Grenoble, France, for granting SAXS beam time (Project No. SC-4621 at the ID02 beamline). The help of Dr. Alessandro Mariani at the ID02 is also gratefully acknowledged. Computational resources were provided by the CESNET LM2015042 and the CERIT Scientific Cloud LM2015085, provided under the programme “Projects of Large Research, Development, and Innovations Infrastructures”.

quenching of 5-(N-dodecanoyl)aminofluorescein embedded in mPNIPAm micelles by DPCl) indicated that DP+ ions strongly binds to the micelles. SAXS measurement revealed the twostep growth of the core size with increasing amount of DPCl in mPNIPAm micelles: (i) In the first step (up to Z = 2) the core size increase was caused by the solubilization of aliphatic tails of DP+ ions in the micellar core (Scheme 3b). (ii) In the second step (above Z = 2), the increase of the dense central part of micelles occurred as a result of dehydration of the inner part of PNIPAm chains, which then intermixed with dodecyl groups of the surfactant and formed a dense layer around the original core (Scheme 3c). While the first step was faithfully reproduced by DPD simulations, further increase in Z was not well emulated: instead of the core swelling, DPD predicts gradual disruption of micelles. The DPD simulation thus showed that a simple coarse-grained model can satisfactorily describe the coassembling behavior of complex systems based on the interplay of electrostatic and hydrophobic effects, but the simulation data have to be interpreted carefully in cases when specific interactions (such as hydrogen bonds) play important role. The performed study thus demonstrated both the strength and limits of coarse-grained DPD simulations. It clearly showed that the simulations based on a simple model, which does not take specific interactions (hydrogen bonds) into account, allow one to identify the effects caused by specific interactions, help to understand their mechanism and judge the role they play in the studied system. In summary, the study shows that the presence of charged groups at the ends of mPNIPAm chains appreciably modifies the behavior, but its assembly with cationic DPCl surfactant is dominated by hydrophobic interactions.

■

REFERENCES

(1) Schild, H. G. Poly (n-isopropylacrylamide) - experiment, theory and application. Prog. Polym. Sci. 1992, 17, 163−249. (2) Roy, D.; Brooks, W. L. A.; Sumerlin, B. S. New directions in thermoresponsive polymers. Chem. Soc. Rev. 2013, 42, 7214−7243. (3) Halperin, A.; Kroeger, M.; Winnik, F. M. Poly(N-isopropylacrylamide) Phase Diagrams: Fifty Years of Research. Angew. Chem., Int. Ed. 2015, 54, 15342−15367. (4) Hu, Z. B.; Xia, X. H.; Marquez, M.; Weng, H.; Tang, L. P. Controlled release from and tissue response to physically bonded hydrogel nanoparticle assembly. Macromol. Symp. 2005, 227, 275− 284. (5) Jeong, B.; Kim, S. W.; Bae, Y. H. Thermosensitive sol-gel reversible hydrogels. Adv. Drug Delivery Rev. 2002, 54, 37−51. (6) Klouda, L. Thermoresponsive hydrogels in biomedical applications A seven-year update. Eur. J. Pharm. Biopharm. 2015, 97, 338−349. (7) Wei, H.; Cheng, S.-X.; Zhang, X.-Z.; Zhuo, R.-X. Thermosensitive polymeric micelles based on poly(N-isopropylacrylamide) as drug carriers. Prog. Polym. Sci. 2009, 34, 893−910. (8) Talelli, M.; Hennink, W. E. Thermosensitive polymeric micelles for targeted drug delivery. Nanomedicine 2011, 6, 1245−1255. (9) Xue, N.; Qiu, X.-P.; Chen, Y.; Satoh, T.; Kakuchi, T.; Winnik, F. M. Effect of Chain Architecture on the Phase Transition of Star and M


Article

Macromolecules Cyclic Poly(N-isopropylacrylamide) in Water. J. Polym. Sci., Part B: Polym. Phys. 2016, 54, 2059−2068. (10) Luo, S. Z.; Xu, J.; Zhu, Z. Y.; Wu, C.; Liu, S. Y. Phase transition behavior of unimolecular micelles with thermoresponsive poly(Nisopropylacrylamide) coronas. J. Phys. Chem. B 2006, 110, 9132− 9139. (11) Xia, Y.; Burke, N. A. D.; Stover, H. D. H. End group effect on the thermal response of narrow-disperse poly(N-isopropylacrylamide) prepared by atom transfer radical polymerization. Macromolecules 2006, 39, 2275−2283. (12) Nuopponen, M.; Ojala, J.; Tenhu, H. Aggregation behaviour of well defined amphiphilic diblock copolymers with poly (Nisopropylacrylamide) and hydrophobic blocks. Polymer 2004, 45, 3643−3650. (13) Ye, X. D.; Fei, J. Y.; Guan, J.; Zhou, X. C.; Zhang, G. Z. Dispersion of Polystyrene Inside Polystyrene-b-poly(N-isopropylacrylamide) Micelles in Water. J. Polym. Sci., Part B: Polym. Phys. 2010, 48, 749−755. (14) Lopez-Fontal, E.; Grochmal, A.; Foran, T.; Milanesi, L.; Tomas, S. Ship in a bottle: confinement-promoted self-assembly. Chem. Sci. 2018, 9, 1760−1768. (15) Adelsberger, J.; Kulkarni, A.; Jain, A.; Wang, W.; BivigouKoumba, A. M.; Busch, P.; Pipich, V.; Holderer, O.; Hellweg, T.; Laschewsky, A.; Mueller-Buschbaum, P.; Papadakis, C. M. Thermoresponsive PS-b-PNIPAM-b-PS Micelles: Aggregation Behavior, Segmental Dynamics, and Thermal Response. Macromolecules 2010, 43, 2490−2501. (16) Papagiannopoulos, A.; Zhao, J.; Zhang, G.; Pispas, S.; Radulescu, A. Thermoresponsive aggregation of PS-PNIPAM-PS triblock copolymer: A combined study of light scattering and small angle neutron Scattering. Eur. Polym. J. 2014, 56, 59−68. (17) FitzGerald, P. A.; Gupta, S.; Wood, K.; Perrier, S.; Warr, G. G. Temperature- and pH-Responsive Micelles with Collapsible Poly(Nisopropylacrylamide) Headgroups. Langmuir 2014, 30, 7986−7992. (18) Skvarla, J.; Raya, R. K.; Uchman, M.; Zednik, J.; Prochazka, K.; Garamus, V. M.; Meristoudi, A.; Pispas, S.; Stepanek, M. Thermoresponsive behavior of poly(N-isopropylacrylamide)s with dodecyl and carboxyl terminal groups in aqueous solution: pHdependent cloud point temperature. Colloid Polym. Sci. 2017, 295, 1343−1349. (19) Alargova, R. G.; Kochijashky, I. I.; Sierra, M. L.; Zana, R. Micelle aggregation numbers of surfactants in aqueous solutions: A comparison between the results from steady-state and time-resolved fluorescence quenching. Langmuir 1998, 14, 5412−5418. (20) Van Vaerenbergh, P.; Leonardon, J.; Sztucki, M.; Boesecke, P.; Gorini, J.; Claustre, L.; Sever, F.; Morse, J.; Narayanan, T. An Upgrade Beamline for Combined Wide, Small and Ultra Small-Angle X-ray Scattering at the ESRF. In Proceedings of the 12th International Conference on Synchrotron Radiation Instrumentation; Shen, Q., Nelson, C., Eds.; 2016; Vol. 1741. (21) Bressler, I.; Kohlbrecher, J.; Thunemann, A. F. SASfit: a tool for small-angle scattering data analysis using a library of analytical expressions. J. Appl. Crystallogr. 2015, 48, 1587−1598. (22) Matejicek, P.; Uhlik, F.; Limpouchova, Z.; Prochazka, K.; Tuzar, Z.; Webber, S. Experimental study of hydrophobically modified amphiphilic block copolymer micelles using light scattering and nonradiative excitation energy transfer. Macromolecules 2002, 35, 9487−9496. (23) Stepanek, M.; Prochazka, K.; Brown, W. Time-dependent behavior of block polyelectrolyte micelles in aqueous media studied by potentiometric titrations, QELS and fluorometry. Langmuir 2000, 16, 2502−2507. (24) Delisavva, F.; Uchman, M.; Skvarla, J.; Wozniak, E.; Pavlova, E.; Slouf, M.; Garamus, V. M.; Prochazka, K.; Stepanek, M. Influence of Corona Structure on Binding of an Ionic Surfactant in Oppositely Charged Amphiphilic Polyelectrolyte Micelles. Langmuir 2016, 32, 4059−4065. (25) Zhao, J.; Zhang, G.; Pispas, S. Thermo-Induced Aggregation Behavior of Poly(ethylene oxide)-b-poly(N-isopropylacrylamide)

Block Copolymers in the Presence of Cationic Surfactants. J. Phys. Chem. B 2009, 113, 10600−10606. (26) Jelinek, K.; Limpouchova, Z.; Uhlik, F.; Prochazka, K. SCF study of Amphiphilic micellar shells containing polyelectrolyte and hydrophobic sequences. Macromolecules 2007, 40, 7656−7664. (27) Langevin, D. Complexation of oppositely charged polyelectrolytes and surfactants in aqueous solutions. A review. Adv. Colloid Interface Sci. 2009, 147−48, 170−177. (28) Posel, Z.; Limpouchova, Z.; Sindelka, K.; Lisal, M.; Prochazka, K. Dissipative Particle Dynamics Study of the pH-Dependent Behavior of Poly(2-vinylpyridine)-block-poly(ethylene oxide) Diblock Copolymer in Aqueous Buffers. Macromolecules 2014, 47, 2503−2514. (29) Sindelka, K.; Limpouchova, Z.; Lisal, M.; Prochazka, K. Dissipative Particle Dynamics Study of Electrostatic Self-Assembly in Aqueous Mixtures of Copolymers Containing One Neutral WaterSoluble Block and One Either Positively or Negatively Charged Polyelectrolyte Block (vol 47, pg 6121, 2012). Macromolecules 2014, 47, 7252. (30) Sindelka, K.; Limpouchova, Z.; Lisal, M.; Prochazka, K. The electrostatic co-assembly in non-stoichiometric aqueous mixtures of copolymers composed of one neutral water-soluble and one polyelectrolyte (either positively or negatively charged) block: a dissipative particle dynamics study. Phys. Chem. Chem. Phys. 2016, 18, 16137−16151. (31) Sindelka, K.; Limpouchova, Z.; Lisal, M.; Prochazka, K. Dissipative Particle Dynamics Study of Electrostatic Self-Assembly in Aqueous Mixtures of Copolymers Containing One Neutral WaterSoluble Block and One Either Positively or Negatively Charged Polyelectrolyte Block. Macromolecules 2014, 47, 6121−6134. (32) Lisal, M.; Limpouchova, Z.; Prochazka, K. The self-assembly of copolymers with one hydrophobic and one polyelectrolyte block in aqueous media: a dissipative particle dynamics study. Phys. Chem. Chem. Phys. 2016, 18, 16127−16136. (33) Hoogerbrugge, P. J.; Koelman, J. M. V. A. Simulating microscopic hydrodynamic phenomena with dissipative particle dynamics. Europhys. Lett. 1992, 19, 155−160. (34) Koelman, J. M. V. A.; Hoogerbrugge, P. J. Dynamic simulations of hard-sphere suspensions under steady shear. Europhys. Lett. 1993, 21, 363−368. (35) Groot, R. D.; Warren, P. B. Dissipative particle dynamics: Bridging the gap between atomistic and mesoscopic simulation. J. Chem. Phys. 1997, 107, 4423−4435. (36) Groot, R. D. Electrostatic interactions in dissipative particle dynamics-simulation of polyelectrolytes and anionic surfactants. J. Chem. Phys. 2003, 118, 11265−11277. (37) Ibergay, C.; Malfreyt, P.; Tildesley, D. J. Electrostatic Interactions in Dissipative Particle Dynamics: Toward a Mesoscale Modeling of the Polyelectrolyte Brushes. J. Chem. Theory Comput. 2009, 5, 3245−3259. (38) Warren, P. B.; Vlasov, A. Screening properties of four mesoscale smoothed charge models, with application to dissipative particle dynamics. J. Chem. Phys. 2014, 140, 084904. (39) Meneses-Juarez, E.; Marquez-Beltran, C.; Rivas-Silva, J. F.; Pal, U.; Gonzalez-Melchor, M. The structure and interaction mechanism of a polyelectrolyte complex: a dissipative particle dynamics study. Soft Matter 2015, 11, 5889−5897. (40) Bates, F. S. Polymer-polymer phase-behavior. Science 1991, 251, 898−905. (41) Seaton, M. A.; Anderson, R. L.; Metz, S.; Smith, W. DL_MESO: highly scalable mesoscale simulations. Mol. Simul. 2013, 39, 796−821. (42) Gonzalez-Melchor, M.; Mayoral, E.; Velazquez, M. E.; Alejandre, J. Electrostatic interactions in dissipative particle dynamics using the Ewald sums. J. Chem. Phys. 2006, 125, 224107. (43) Uhlik, F.; Limpouchova, Z.; Jelinek, K.; Prochazka, K. Polyelectrolyte shells of copolymer micelles in aqueous solutions: A Monte Carlo study. J. Chem. Phys. 2004, 121, 2367−2375. (44) Rudnick, J.; Gaspari, G. The shapes of random-walks. Science 1987, 237, 384−389. N


Coassembly of Poly(N-isopropylacrylamide) - ACS Publications

Recommend Documents