Synergistic Effects of Bound Micelles and Temperature on the

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Synergistic Effects of Bound Micelles and Temperature on Flexibility of Thermoresponsive Polymer Brush Peng Wei Zhu, and Luguang Chen J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.6b08696 • Publication Date (Web): 17 Oct 2016 Downloaded from http://pubs.acs.org on October 22, 2016

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The Journal of Physical Chemistry

Synergistic Effects of Bound Micelles and Temperature on Flexibility of Thermoresponsive Polymer Brush

Peng–Wei Zhu∗,† and Luguang Chen‡

†

Department of Materials Science and Engineering, ‡Department of Chemical Engineering, Monash University, Clayton, VIC 3800, Australia

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ABSTRACT: A persistence length is a key parameter for the quantitative interpretation of the flexibility of polymers. We have studied the complexes composed of spherical poly(N– isopropylacrylamide) (PNIPAM) brush and sodium dodecyl sulfate (SDS) micelle in efforts to characterize the flexibility of tethered PNIPAM below the lower critical solution temperature TLCST. An analytical mean–field model is utilized to describe the persistence length Lp in a broad range of

ψ, the number of bound micelles per chain. The persistence length of the micelle–constrained PNIPAM is quantitatively correlated with the thermal energy kBT, electrostatic repulsion fC, and effective excluded volume parameter νeff. The persistence length per ψ, which depends on T and fC, is found to scale with the synergistic effect fC/(ψkBT). The results reveal that the micelle bound charges affecting the persistence length are analogues to the fixed charges of polyelectrolytes, though the bound micelles are separated by a large number of neutral monomers. The extension of the micelle–constrained PNIPAM decreases as < L >∼ fC− β F with fC, where βF ≈ 0.58–0.8 depending on ψ, but as the universal power−law < L >∼ ( f C / k BT ) −0.6 with the synergistic effect fC/(kBT), irrespective of ψ. In spite of intricate interplay among the multiple components in the system, the extension scales as a function of νeff as < L >∼ (ν eff /ψLP ) − βV , where βV ≈ 0.35 for the significant monomer interaction and βV ≈ 0.2 for the weak or negligible monomer interaction.


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1. INTRODUCTION Polymer–surfactant complexes in aqueous solutions have been studied over the past several decades since they are tremendous importance in a wide variety of applications.1–5 Complexes can also serve models to understand other more complicated systems, such as protein–surfactant, protein–lipid, and others with respective biological context.1,6,7 When viewed from the interaction strength, polymer–surfactant complexes can be classified as two broad categories: a weakly interacting system comprised of surfactants (mainly anionic) and neutral polymers, and a strongly interacting system comprised of polyelectrolytes and oppositely charged surfactants. From a morphological point of view, particularly when the surfactant concentration c exceeds a critical aggregation concentration (cac), polymer–surfactant complexes are referred to as a pearl–necklace structure. In recent years, the study of polymer−surfactant complexes has been extended to polymers under constrained conditions. Amongst them, polymer brushes are particularly relevant to the current work.8-10 For polymer brushes, since there is a strong fluctuation of segment crowding, the monomer density possesses a parabolic distribution from grafting surfaces to chain ends. In the field of polymer brush−surfactant complexes, most of studies were focused on the polyelectrolyte brush−surfactant system11-13 and the physically adsorbed polymer−surfactant system.14-17 Little attention was given to the system composed of neutral polymer brushes and ionic surfactants. In the literature, there are only few papers reporting the neutral polymer brush–surfactant system. de Vos et al comprehensively investigated the interactions between sodium dodecyl sulfate (SDS) and polyethylene oxide (PEO) planar brush above cac of SDS concentration cSDS.18 Varga et al. reported the effect of grafting density on interactions between bottle PEO brush and SDS.19 On the other hand, Currie et al. theoretically explored the neutral polymer brush–micelle system by using a mean–field model.20 Their work establishes a quantitative description between micelle–dependent excluded volume and so–called stuffed brushes.21,22 Although the assumption that micelles are only bound to the swollen outer layer of neutral polymer brushes is arguable,23 the model is explicitly linked to the measurable parameters of neutral polymer brush–micelle complexes. 3 Environment ACS Paragon Plus


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While some progress has been made in understanding neutral brush–micelle complexes, physical properties of tethered chains, such as the flexibility or stiffness, have not been reported. The flexibility is a key parameter of polymers, which influences properties of polymers utilized as entities or as building blocks for materials. The flexibility of chains also plays a role in controlling some aspects of material functions involving biological contexts.24 Thus, understanding the flexibility of chains renders rational designs to optimise properties of materials. However, a direct measurement of flexibility is still a difficult challenge to polymer brush–micelle complexes. In this paper, we investigate synergistic effects of SDS micelles and temperature on the flexibility of poly(N–isopropylacrylamide) (PNIPAM) covalently tethered to polystyrene nanoparticles when cSDS > cac. The same system was previously studied at cSDS < cac focusing on the density distribution of the brush.25 PNIPAM is a neutral polymer with a lower critical solution temperature (LCST) TLCST (304–308 K).26,27 The present work is carried out in the range of T < TLCST. Compared with PEO, the aqueous solution of PNIPAM can be switched between a swollen state and a collapsed state at TLCST. This thermoresponsive property near ambient temperature makes PNIPAM to become an important water–soluble polymer as utilized for a broad range of applications.26-29 Yet, regarding the flexibility of chains, the thermoresponsive feature makes the quantitative characterization of tethered PNIPAM to be more complicated. Two features of PNIPAM brush–SDS complexes, which are particularly relevant to this paper, are first worth emphasising. The first is about the continuous collapse of tethered PNIPAM at T < TLCST.25,30,31 Apparently, the conformational transition of the tethered PNIPAM is decoupled from the solvent quality. Such a unique phenomenon was considered as a cooperative process32 which can be explained by the n–clusters concept of de Gennes33 or the vertical phase separation of Halperin et al.34,35 This collapse primarily depends on the parameters characterising the brush, including the grafting density σ and the number of monomers N. However, the addition of surfactants, especially the binding of micelles to the PNIPAM brush, can effectively weaken and eventually eliminate attractive interactions among segments due to the electrostatic repulsion. Note that the bound micelles are not shared within chains.36 The second feature is about the location of 4 Environment ACS Paragon Plus

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bound micelles within the PNIPAM brush. Recently, Halperin et al reported that the collapsed PNIPAM brush virtually favours the penetration of particles.23 The authors found that the decrease in the osmotic pressure of the brush reduces the free energy penalty incurred upon inserting. The particles that are expelled from the swollen outer layer can penetrate into the collapsed inner layer.23,37 The remainder of the article is organised as follows. In the next section, the sample preparation and characterization are presented. The analysis and discussion of the experimental data are presented in Section 3. We first use a scaling model38 to describe phenomenologically the minimum force required to stretch a collapsed brush at cSDS < cac. A modified excluded volume of the mean– field model20,21 is then utilized as a model parameter for spherical polymer brushes at cSDS > cac so as to characterize the flexibility–related parameters, i.e., the persistence length and the end–to–end distance. We discuss comprehensively on the factors and their synergies which affect the flexibility of the micelle–constrained PNIPAM, and quantitatively describe their relations. Section 4 summaries our conclusions.

2. EXPERIMENTAL SECTION Materials. N–Isopropylacrylamide (NIPAM) was purchased from Aldrich and purified by recrystallization from a hexane and benzene mixture (65/35 by volume). Styrene (Aldrich) was used immediately after distillation at 328 K under reduced pressure. Azobis(isobutyronitrile) (AIBN) (Aldrich) was recrystallized from alcohol. Potassium persulfate (KPS) (Aldrich), sodium metabisulfite (SMB) (Merck), and sodium dodecyl sulfate (SDS) (Aldrich) were used as received.

Synthesis and Characterization of PNIPAM. PNIPAM was synthesized by radical polymerization in a benzene/acetone (70/30) mixed solvent using AIBN as initiator. The concentration of NIPAM was 100 g/L and AIBN was 0.5% NIPAM by weight. The polymerization was carried out by stirring at 338 K for 20 hours under positive nitrogen pressure. The solvent was evaporated in vacuum at 303 K under nitrogen flow. The dried PNIPAM was dissolved in dry acetone and precipitated by the addition of dry n–hexane. The fractionated PNIPAM samples were 5 Environment ACS Paragon Plus


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recovered by freeze–drying. The first fractionated PNIPAM was used to prepare PNIPAM– polystyrene latex particles. Its molecular weight and radius of gyration were determined to be ∼ 1.3×106 and ∼ 550 Å, respectively.25

Synthesis and Characterization of PNIPAM–PS Latex Particles. The synthesis of PNIPAM tethered to polystyrene particles was carried out in water using a redox initiator (KPS/SMB) at room temperature. For the purpose of the present work, it is necessary to prepare thermally unstable latex particles so that the behaviour of PNIPAM brush is attributed to the addition of SDS. The concentration of PNIPAM was 38 g/L. First, styrene (0.2% PNIPAM by weight) was slowly added dropwise to the PNIPAM solution by stirring under positive nitrogen pressure in the presence of KPS (0.35% styrene by weight) and SMB (0.4% KPS by weight). Then, to generate a clear suspension of latex particles, styrene (0.8% PNIPAM by weight) and the aqueous solution of KPS (1.6% styrene by weight) and SMB (0.4% KPS by weight) were quickly added to the solution under vigorous stirring. The final concentration of PNIPAM was 15 g/L. After ∼ 20 hours, the latex particles were filtered through a Millipore filter (0.8 µm) at room temperature and then dialyzed under stirring by repeated changes of fresh Milli–Q water at 277 K over a period of one week. The free PNIPAM was further removed by centrifugation and decantation of the supernatant at 293 K. The latex particles were redispersed into Milli–Q water and kept at 277 K for about one week before they were filtered through the Millipore filter. The degree of polymerization for tethered PNIPAM and grafting density were previously estimated to be N ≈ 420 and σ ≈ 0.2 chains/nm2.25

Preparation and Characterization of PNIPAM Brush–SDS Complexes. To prepare a desired SDS concentration, cSDS, the concentrated SDS solution was added dropwise by stirring to the PNIPAM–PS latex particles. The samples were kept at 277 K prior to use. The number of SDS molecules bound to PNIPAM was calculated from the binding isotherm reported in the literature.39 For the present work, cac was estimated to be ∼ 0.87 mM,25 which is in the range of literature data.40-45 The results confirm the report that the interaction of SDS with constrained PNIPAM is


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similar to that with free PNIPAM.40 In the literature, the values of cac were 0.69–1.3 mM for linear PNIPAM chains 26,41-43 and 1 mM for PNIPAM microgels.44,45

Figure 1. Degree of micelle coverage Γ and number of micelles per chain ψ versus SDS concentration cSDS.

The degree of surfactant coverage Γ is defined as Γ = ψ N ad / N ,20,21 where Nad is the number of monomers wrapping around the surface of bound micelles and ψ is the number of micelles per chain. The small angle neutron scattering (SANS) measurements showed that the distance between bound SDS micelles with a radius Rm ≈ 16 Å is ∼ 63 Å.36 Nad was accordingly estimated to be ∼ 22.25 ψ was calculated by ψ = surfactant molecules/(Zm × polymer molecules), where Zm is the aggregation number of surfactant molecules within a bound micelle. For PNIPAM–SDS complexes, literature data of Zm are scarce; Zm = 7–8 for linear PNIPAM chains46 and 4–5 for PNIPAM microgels,44 respectively. Considering a constrained environment of polymer brushes, Zm = 5 was used to calculate ψ, the number of bound micelles per chain. These results are shown in Figure 1 as a function of cSDS. Obviously, ψ ≈ 1 corresponding to cSDS = 0.87 mM is consistent with the definition of cac, and thus proves the validity of the ψ – cSDS curve. Once the parameters Nad and ψ were given, the degree of the surfactant coverage Γ was calculated. The results are also shown in Figure 1 as a function of cSDS.



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Measurement of Latex Particles. The hydrodynamic diameter of latex particles, Dh, was determined by dynamic light scattering (DLS). The argon ion laser was operated at a scattering angle

of

90º

with

a

wavelength

of

488

nm.

The

intensity

autocorrelation

function, G ( 2 ) (τ ) ∝ 1 + B g (1) (τ ) ,47 was measured using a Malvern 4700c correlator, where B is a 2

spatial coherence factor and g(1)(τ) is an electric field autocorrelation function. The z–average translational diffusion coefficient Dz was obtained from the analysis of g(1)(τ). The hydrodynamic diameter Dh was calculated from Dz using the Stockes–Einstain equation Dh = k BT /[3πη (T ) Dz ] , where η(T) is the water viscosity at temperature T and kB is the Boltzmann constant. The temperature was controlled with an accuracy of ± 0.1 ºC. The dry nitrogen gas flowed through the sample chamber to prevent moisture condensation at lower temperatures. The concentration of latex particles was ∼ 5×10−4 g/cm3. The thermal stability was examined by repeated measurements of Dh. In the absence of SDS, Dh increased significantly at ∼ 304.6 K, which was adopted as TLCST. The minimum cSDS required to prevent latex particles from aggregation was cSDS ≈ 0.1 mM. Before the DLS measurement, the latex particles were thermally equilibrated at a given temperature for at least 20 min. The value of Dh was a mean value of 3–6 measurements, depending on the temperature. The average radius of PS particles was r ≈ 800 Å measured by transmission electron microscopy (TEM). The brush height h was obtained by h = ( Dh / 2 − r ) . At cSDS ≈ 0.1 mM, Dh was ∼ 844 Å at 333 K. The solid fractions per latex particle were (400/422)3 ≈ 0.85 and 0.15, respectively, corresponding to the PS core and the PNIPAM corona.

3. RESULTS AND DISCUSSION Temperature Dependence of Brush Height. The brush height is shown in Figure 2 as a function of temperature in different values of ψ (cSDS > cac). For the sake of comparison, the brush height at cSDS = 0.25 mM (< cac) is as well included. In the absence of bound micelles, cSDS = 0.25 mM, the PNIPAM brush continuously collapses from 600 Å at 276 K to 210 Å near TLCST. In the absence of surfactant, or cSDS = 0, the latex particles aggregates near TLCST.25 The collapse occurring below 8 Environment ACS Paragon Plus

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TLCST, as aforementioned, is initiated by the n–clusters or vertical phase separation in the inner dense layer of the PNIPAM brush.33–35

Figure 2. Brush height h versus temperature T at different ψ (cSDS > cac). Filled squares are the brush height h at cSDS = 0.25 mM (cSDS < cac).

When cSDS > cac, the pearl–necklace structure forms. The collapsed brush at cSDS = 0.25 mM is effectively stretched to a temperature–independent height (Figure 2), irrespective of ψ. However, the plateau of brush height slightly increases with increasing ψ from 2 to 5.2. A further increase of

ψ, the height does not change, indicating a stretching limit of the brush. In this situation, the free chain ends are expected to be brought into the outer region of the brush. The electrostatic repulsion greatly reduces the n–clusters or vertical phase separation, which eventually eliminates the driving force for the collapse, leading to a fairly homogeneous brush. The bound micelles are separated by a mean distance along the backbone, as indicated by the SANS experiments.36 Assume that the bound micelles break up a tethered chain into a number of strings along the backbone, each of which is connected by the average number of monomers nm = (N - ψNad)/ψ. While the micelle–constrained PNIPAM extends, the partial collapse is expected to occur in the outer edge of the brush as well as the vicinity of the grafting surface, because the segments there are less influenced by the bound micelles.



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The results are consistent with the theoretical description that the collapsed PNIPAM favours the penetration and adsorption of particles.23,37 If the binding of SDS micelles occurred only in the swollen outer layer, the PNIPAM brush would not be stretched to a temperature–independent height, especially at higher temperatures, because the n–clusters or vertical phase separation would remain in the dense inner layer. Since the osmotic pressure and inserted volume increase with increasing the distance from the grafting surface,23 the binding of SDS micelles to the PNIPAM brush is suggested to successively proceed from the inner layer to the outer layer.

Brush Conformations at cSDS < cac. Before a quantitative characterization of micelle constrained PNIPAM strings, we first use the theoretical model of Halperin and Zhulina38 to predict the minimum force required to pull the collapsed layer at cSDS < cac to the stretched brush at cSDS > cac. To make for convenient comparison, the blob picture is used to describe the brush, which is schematically shown in Figure 3a. The spherical PNIPAM brush at T < TLCST is illustrated as a tadpole–like model comprising a collapsed ″head″ of Ng monomers and a strongly stretched ″tail″ of Ns = N - Ng monomers,38,48 i.e., the collapsed and stretched layers are coexistence at cSDS < cac. The collapsed layer is pictured as a globule of size Rglob = aN 1g / 3τ −1 / 3 , where a = 3 Å is the monomer size49 and τ = (TLCST / T − 1) is an effective temperature measuring the deviation from TLCST. The brush height h at cSDS < cac is the sum of globule size Rglob and stretched length hs (Figure 3a) When cSDS < cac, Ng increases with temperature by accreting the monomer from the stretched layer. When cSDS > cac, hs extends by pulling the monomer out of the collapsed layer. Halperin and Zhulina investigated polymers tethered to parallel and flat surfaces separated by a distance .38 By analysing the surface energy and utilizing the tensile–blob concept,50 they described three regimes as a course of unfolding a collapsed brush. The second regime is a tadpole– like conformation and the restoring force of collapsed layer is given by38 f RC

 < l > N g a2  ≈ k BT  + σ  N g a2 < l >   


(1)

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where kB is the Boltzmann constant.

Figure 3. (a) Schematic illustration of a tadpole model comprising a collapsed layer or “head” and a stretched layer or “tail” at T < TLCST. In case ii, bound micelles are omitted for clarity. (b) Restoring forces f RC (filled triangles) for collapsed layer and f RS (filled down triangles) for stretched layer as a function of temperature T.



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We envision that the micelle–constrained PNIPAM strings are similar to the tethered chains between two plates. The tadpole–like conformation of PNIPAM brush at cSDS < cac is thus under two solvent conditions: the collapsed layer or ″head″ is in a poor solvent but the stretched layer or ″tail″ is in a good solvent (Figure 3a). Considering the transition from the tadpole–like conformation at cSDS < cac to the strongly stretched brush at cSDS > cac (Figure 2), the minimum force required to unravel the collapsed laye is approximately equal to the restoring force of the collapsed layer. As such, = ∆h (Figures 2 and 3a) and Ng ≈ ∆h/a; eq 1 is given by f RC = k BT (1 / a + aσ ) . Figure 3b shows that f RC increase with increasing temperature. Obviously, the greater force is needed to pull out the monomer from the collapsed layer containing the stronger monomer interaction. Note that the variation of f RC with temperature is not significant: the magnitude of f RC is changed from ∼ 12.9 at 277 K to ∼ 14.3 pN near TLCST. Gunari et al.51 performed force–extension measurements of polystyrene in water. Their experiments confirmed three regimes for the transition from the globule to the stretched chain. They found that the force required to unravel the polystyrene globule in water is ∼ 13 pN at room temperature. Since the restoring force of collapsed segments is independent of chemical nature, our results are comparable to their work. On the other hand, the strongly stretched layer of the tadpole–like conformation is in good solvent condition. The restoring force of swollen brush f RS is given by38 S

fR

k T  h  ≈ 3B/ 5  3 /s5  Ns a  Ns a 

3/ 2

(2)

where Ns = (N - ∆h/a) and = hs = h - Rglob (Figure 3a). We use eq 2 to predict the restoring force f RS of stretched layer. The results are also shown in Figure 3b. In good solvent conditions, the restoring force of stretched layer is not larger than 4.3 pN. With increasing temperature, f RS is diminished to zero near TLCST, corresponding to the experimental observation (Figure 2) that almost all monomers are incorporated into the collapsed layer. 12 Environment ACS Paragon Plus

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Model of Neutral Brush–Micelle Complexes. Although the PNIPAM brush is strongly stretched due to the electrostatic repulsion of bound micelles (Figure 2), it is not feasible to directly characterize the flexibility of tethered PNIPAM chains. In this situation, the mean–field model20 paves the way for indirect studies on the flexibility of micelle–constrained PNIPAM. In the following, we brief the scaling model of spherical polymer brushes and modify the excluded volume parameter by incorporating the electrostatic excluded volume. To characterize the flexibility, we use the modified excluded volume parameter as an input parameter of the scaling model to calculate the persistence length of micelle–constrained PNIPAM. Alexander52 and de Gennes53 (AdG), in their pioneering work, described polymer chains grafted to a planar surface by using scaling theory. Daoud and Cotton (DC) extended the AdG model to a star polymer in which polymer chains are spherically symmetric around a central grafting point.54 The DC model was later developed to characterize polymers tethered to the curved (convex) surface, 55,56

giving rise to the height of spherical polymer brushes

h = a ( 4πσν r 2 N 3 )1 / 5

(3)

where the dimensionless variable ν is an excluded volume parameter. The brush height is controlled by a balance between the restoring force, which favours a compact conformation, and the excluded volume interaction, which favours an extended conformation. For a given spherical polymer brush, the excluded volume parameter ν plays a crucial role in controlling the brush conformation or brush height. One can tune ν, for example, by varying solvent quality, adding suitable particles or both. In this case, the excluded volume parameter is denoted by the effective excluded volume parameter νeff, accounting for the influence of inserted particles. In this paper, the contribution of bound micelles to νeff not only involves the inserted volume but also the electrostatic repulsion. These two factors lead to the tremendous expansion of spherical PNIPAM brush. Consequently, the brush is strongly stretched to a temperature–independent height (Figure 2). Currie et al treated micelles as hard nanoparticles which modify the excluded volume of polymer brushes upon binding.20 Their model elaborates three terms characterizing effects of bound micelles 13 Environment ACS Paragon Plus


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on the excluded volume parameter: (i) the monomer interaction νmonomer, (ii) the micelle interaction

νmicelle, and (iii) the monomer–micelle interactionνmonomer–micelle. The effective excluded volume parameter νeff is related to the micelle coverage Γ within the brush20

ν eff = (1 − Γ )2ν monomer + Γ 2ν micelle + Γ (1 − Γ )ν monomer − micelle

(4)

ν eff = ν monomer = ν when Γ = 0. The contribution of monomer interaction to νeff, or νmonomer, is proportional to the effective temperature τ 23

ν monomer =

Lp a

τ=

L p TLCST ( − 1) a T

(5)

where Lp is the persistence length, which is mathematically defined as an exponential decay length of tangent–tangent correlations.57 As such, Lp/a is the number of monomers constituting a persistence length. Physically, the persistence length quantifies the flexibility of a chain molecule at a small length scale: the longer the persistence length is, the stiffer the polymer chain is. The second term of eq 4 is the contribution of bound micelle interaction to νeff. Assume that a micelle is an impenetrable or hard spherical particle, νmicelle is given by

vmicelle =

4πκ −1L2p 16π −1 3 κ R + + m 2 2 3ν 0 N ad ν 0 N ad

(

)

(6)

where Rm is the average radius of bound micelles, ν0 is the excluded volume of hard spherical particle, and κ-1 is the Debye screening length. For monovalent electrolytes, such as SDS, the Debye screening length κ-1 is given by:

κ

−1

 ε k BT =  2  e Z m N AcSDS

  

1/2

(7)

where e is the electron charge, NA is the Avogadro constant, and ε is the permittivity of water. The charges of individual micelles are assumed to be a point charge. Rm and κ-1 depend on temperature. The radius of the SDS micelle decreases linearly with increasing temperature,58 giving Rm =

31.74341 - 0.05007×T in a unit of angstrom. The temperature–dependent κ-1 can be calculated from 14 Environment ACS Paragon Plus

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the temperature–dependent ε=5321/T + 233.76 - 0.9297×T + 0.001417×T2 - 0.8292T-6×T3.59 Eq 6 is normalized by the excluded volume of a hard sphere, ν 0 = 8

4π 3 20,21 The concept of the a . 3

electrostatic excluded volume60 is encompassed to the second term of eq 6, accounting for the effect of electrostatic repulsion on the persistence length of neutral polymer chains. The third term of eq 4 is the contribution of micelle–monomer interaction to νeff when the surface of bound micelle is wrapped around by polymer segments. νmonomer–micelle is given by

vmonomer − micelle =

Lp 2π Rm3 + τ 3ν 0 N ad 2a

(8)

Note that the second term of eq 8 is not negligible, as compared to Rm, because the persistence length can be much larger than the radius of bound micelles with temperature. The effective excluded volume parameter νeff is inputted into eq 3 to calculate the brush height h. In the absence of bound micelles, the height of spherical brush is given by h = a 4 / 5[ 4πσL p (TLCST / T − 1) r 2 N 3 ]1 / 5 . The persistence length Lp is only unknown parameter in eqs 5–8. We perform a data fitting by adjusting Lp to the experimental data of brush height h (Figure 2). Since the length of micelle– constrained PNIPAM strings depends on the number of bound micelles per chain ψ, we use the relative persistence length lp = Lp/Lc for the sake of comparison, where Lc ≈ a(N - ψNad)/ψ is a contour length between the bound micelles. In the following sections, we first discuss, respectively, how the temperature and the bound micelle influence the persistence length, which is followed by their synergistic effects.

Temperature Dependence of Persistence Length. The relative persistence length is presented in Figure 4a as a function of temperature. With increasing temperature, lp = Lp/Lc increases until it reaches a maximum near TLCST. The temperature dependence of lp covers a wide range of ψ: ψ = 2 is a minimum number of bound micelles required to form the pearl–necklace structure, whereas statistically ψ = 6.6 divides a tethered chain into six micelle–constrained strings. Note that at higher temperatures the persistence length at ψ = 6.6 exceeds the contour length. The persistence length is



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associated with the conformational feature in two limits.57 When Lp > Lc the chain behaves like a rod. Accordingly, the micelle–constrained PNIPAM is fairly flexible at ψ =2, whereas the observation of Lp > Lc signifies the emergence of rod–like conformation at ψ = 6.6.

Figure 4. (a) Relative persistence length Lp/Lc versus temperature T. (b) Relative end–to–end distance Re/Lc versus temperature T.

The micelle–constrained PNIPAM string is a short length scale and therefore viewed as semiflexible segments. The flexibility is also evaluated by the end–to–end distance between the bound micelles, Re. The end–to–end distance is usually described by the wormlike chain (WLC) model of Kratky–Porod, accounting for the intermediate behaviour between a rigid rod and a flexible coil. In 2–dimensions, the mean square end–to–end distance is given by57 16 Environment ACS Paragon Plus

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 L   L   Re2 = 2 Lp Lc 1 − p 1 − exp − c    L  p   Lc    

(9)

The Kratky–Porod model includes bending fluctuations allowing a chain to deform at a short length scale. The relative end–to–end distance Re/Lc is shown in Figure 4b as a function of temperature. In general, the temperature dependence of Re/Lc is analogous to Lp/Lc. It is however noted that unlike the persistence length, the end–to–end distance is always aligned with the direction of force.57 With regard to the force–extension behaviour, which will be addressed later, the end–to–end distance characterises the extension of micelle–constrained PNIPAM subject to the electrostatic repulsion. The reports on the temperature–enhanced persistence length are few in the literature. In a recent study, Kouwer et al. investigated smart biomimetic gels incorporating polyisocyanopeptides with a tunable LCST.61 They found that the persistence length of polymer chains constituting biomimetic gels increases with temperature. The temperature–enhanced persistence length was also observed from the single–stranded DNA under the greater force.62 Yet, there is a lack of studies concerned with the temperature–dependent persistence length in polymer brush–micelle complexes.

Bound–Micelle Dependence of Persistence Length. It is clear from the previous sections that the temperature–dependent persistence length becomes accessible because the self–repulsion of bound micelles underpins the tethered chains. As such, Lp is considered as a total persistence length containing two contributions: one from the temperature and another from the bound micelle charge. In this section, our discussion concerns the micelle–charge dependence of the persistence length. The effect of electrostatic repulsion on the flexibility of polymer chains can be analysed in the framework of polyelectrolytes.63,64 By calculating the difference in the electrostatic energy between the rod–like configuration and the slightly bent configuration, Odijk65 and, independently, Skolnick and Fixman66 (OSF) proposed an electrostatic persistence length to describe the charge–dependent flexibility. The electrostatic persistence length of the OSF theory, LOSF, is quantitatively described by LOSF = l B /( 4κ 2b 2 ) , where lB is the Bjerrum length and b is the distance between neighbouring 17 Environment ACS Paragon Plus


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charges. The total persistence length of polyelectrolyte chains typically is a sum of electrostatic persistence length and intrinsic (bare) persistence length.65,66 Accordingly, in our work, the persistence length Lp of the micelle–constrained PNIPAM is also considered as a sum of two contributions, or

L p = L p ,T + L p , e

(10)

where Lp,T is the contribution of thermoresponsive feature, belonging the intrinsic property of PNIPAM, and Lp,e is the contribution of bound micelle charges. At a given Lp, the charge– dependent Lp,e can be estimated if the temperature–dependent Lp,T is known. It is worth noting that there are differences between a pearl–necklace chain and a polyelectrolyte chain. For a pearl necklace chain, the charges of bound micelles are separated by a large number of neutral monomers. For a polyelectrolyte chain, the fixed charges are only separated by a short distance of neighbouring sites b. Specifically, the extensibility of micelle–constrained PNIPAM brush is restricted by temperature, whereas the extensibility of polyelectrolytes usually depends on added salts.63 The data of Lp,T are taken from the literature in a range of temperatures 298.1–303.8 K.27 It is known from the literature that Lp,T is infinite or immeasurable when T > 303.8 K. Assuming that

Lp,T is a constant at lower temperatures, we perform a data fitting, over the same range of temperatures as illustrated in Figure 4, to obtain a curve of temperature–dependent Lp,T. We then calculate the charge–dependent Lp,e by using eq 10. This procedure is exemplified in Figure 5a. Figure 5b shows lp,e = Lp,e/Lc as a function of temperature in different values of ψ. As can be seen, the curve shape of Lp,e is analogous to that of Lp, rather than Lp,T. Obviously, the electrostatic repulsion is a dominant contribution to the growth of the persistence length. There is a dramatic decrease in lp,e in a very narrow range of temperatures, which is attributed to the very large value of

Lp,T near TLCST reported in the literature. To further discuss the effect of bound micelles on the flexibility, we quantitatively correlate the persistence length to the Coulomb force fC. The average distance between the bound micelles is 18 Environment ACS Paragon Plus

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approximated by (Re + 2Rm). The charges of individual bound micelles are assumed to be a point charge. The Coulomb force fC imposed at the micelle–constrained PNIPAM string is thus given by

f C = ke

(Z me)2

(Re + 2 Rm )2

(11)

where ke is the Coulomb constant. It is should be pointed out that as the micelle–constrained PNIPAM is stretched, the Coulomb force accordingly decrease because the distance between the bound micelles increases.

Figure 5. (a) Persistence length Lp versus temperature T at ψ = 3.7. Data of temperature–dependent persistence length Lp,T (filled squares) were taken from the literature.27 The inset shows the charge– dependent persistent length Lp,e and its fraction in Lp, Lp,e/Lp, versus T. (b) Relative charge– dependent persistence length Lp,e/Lc versus temperature T.



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The relative persistence length is shown in Figure 6 as a function of the Coulomb force. The electrostatic repulsion here is regarded as an internal force, because the bound–micelles are a part of the pearl–necklace structure. It can be seen that lp scales with fC as l p ∼ f C−α (Figure 6a). The exponent α is found to increase from ∼ 1.4 to ∼ 4.2 with ψ. The lp,e–fC curves exhibit the similar power–law behaviour (Figure 6b) but give rise to larger values of the exponent α, indicating the influence of electrostatic repulsion on the persistence length. When viewed from the force– extension, the results illustrated in Figure 6 are considered as a reverse situation of the chain extension subject to an external force.

Figure 6. Relative persistence length versus Coulomb force fC: (a) Lp/Lc and (b) Lp,e/Lc.

Synergistic Effects of Temperature and Micelle on Persistence Length. In the preceding sections, the description of the flexibility is limited to either the temperature dependence or the 20 Environment ACS Paragon Plus

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force dependence. In this section, we examine the synergistic effect of T and fC on the persistence length. The aim is to explore a unified picture of all the experimental data so as to establish explicit relations characterising the persistence length of micelle–constrained PNIPAM. With this in mind, we introduce the dimensionless variable, afC/(ψkBT), as the synergistic effect between the thermal energy kBT and the Coulomb force fC.

Figure 7. (a) Persistence length per ψ, Lp/ψ, versus afC/(ψkBT). (b) Charge–dependent persistence length per ψ, Lp,e/ψ, versus afC/(ψkBT). Insets are logarithmic plots of the same data.

For the thermoresponsive PNIPAM brush–micelle complexes, the variable afC/(ψkBT) is virtually combined by two competing forces. The thermal energy kBT is the driving force for the conformational collapse, whereas the Coulomb force fC is the driving force for the conformational extension. At a given temperature, when the electrostatic repulsion is greater than the restoring 21 Environment ACS Paragon Plus


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force, the tethered PNIPAM is stretched until the force balance is reached. This is the situation in this paper. On the other hand, when the restoring force is greater than the electrostatic repulsion, the tethered PNIPAM is expected to contract or collapse, leading to the disbanding of the pearl– necklace structure. This situation is beyond the scope of this paper and will be reported separately. Figure 7a shows the persistence length per ψ as a function of afC/(ψkBT). It is seen that the Lp/ψ– afC/(ψkBT) data are approximately superposed on a master curve. The logarithmic plot of the data gives a slope of -1.5, yielding L p /ψ ∼ (af C /ψk BT )

−1.5 ± 0.2

. The similar behaviour is observed from

the charge–dependent Lp,e. The decay part of the (Lp,e/ψ)–afC/(ψkBT) data is approximated by L p, e /ψ ∼ (af C /ψk BT )

−2.4 ± 0.4

Particularly, from these two power–law relations, the contribution of

bound charges to the total persistence length is thus expressed by L p , e / L p ∼ (af C /ψk BT )

−0.9

. Also,

from the Debye screening length κ-1 (eq 7) and the Coulomb force fC (eq 11), we have κ −2 = εke Z m ( fC / k BT ) /[( Re + 2 Rm ) 2 N AcSDS ] or simply κ −2 ∼ ( f C / k BT ) . −1

−1

The comparison of κ −2 ∼ ( f C / k BT )

−1

to L p ,e / L p ∼ (af C /ψk BT )

−0.9

leads to the power–law

L p ,e / L p ∼ κ −1.8 , which links the contribution of the bound charge to the persistence length with the Debye screening length. This power–law presents the physical meaning similar to the power–law

LOSF ∼ κ −2 predicted by the OSF theory.65,66 Accordingly, in spite of the fact that the bound micelles are separated by a large number of neutral monomers, the result suggests that the bound charges affecting the persistence length bear a resemblance to the fixed charges of polyelectrolytes.

Synergistic Effects of Temperature and Micelle on Extension. With regard to the force– extension behaviour, the polymer chains are required to extend along the direction of the force. When viewed in this light, the persistence length is by no means entirely satisfactory when characterizing the force–extension behaviour. As the exponential decay length of tangent–tangent correlations, the persistence length is not necessarily aligned with the force direction. As such, the relative end–to–end distance, Re/Lc, is utilized to quantify the extension because Re is 22 Environment ACS Paragon Plus

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consistently oriented to the direction of the force. In addition to the temperature and electrostatic force, in this section, we also discuss the effect of the excluded volume on the force–extension behaviour of micelle–constrained PNIPAM. We begin with discussing the relation between the extension and the force. Figure 8a shows logarithmic plots of (= Re/Lc) as a function of fC. The extension decreases with the force fC as < L >∼ fC− β F . The negative scaling denotes an inversely proportional relation between fC and . The exponent βF is found to increase from 0.58 to 0.8 with increasing ψ (inset of Figure 8a). In other words, as the repulsive interaction increases, the fairly flexible PNIPAM with βF ≈ 0.58 is extended to the highly rigid PNIPAM with βF ≈ 0.8.

Figure 8. (a) Logarithmic plots of extension = Re/Lc versus Coulomb force fC. The inset shows exponent βF versus ψ. (b) Logarithmic plots of extension = Re/Lc versus afC/(kBT).



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We further examine the synergistic effect of kBT and fC on the extension of micelle– constrained PNIPAM. Figure 8b reveals that the extension scales with afC/(kBT) as a universal power–law < L >∼ (afC / k BT )−0.6 , irrespective of ψ. It is noted that phenomenologically the – afC/(kBT) relation is an inverse situation of the conventional force–extension.50,67,68 Finally, in this section, we address the effect of the excluded–volume on the force–extension behaviour. This is a challenging issue which involves the interplay among the multiple components in the system. In the absence of added particles, stretching a chain implies that its size along the direction of the force is increasingly larger than the width of its backbone. Consequently, the excluded volume of the monomer interaction accordingly diminishes. Particularly, when the chain is strongly stretched to a certain extent, the excluded volume of the monomer interaction is expected to be eventually too small to influence a further extension of the chain.69,70 However, for the PNIPAM brush–SDS micelle complexes, the excluded–volume effect is more complicated. Increasing the number of bound micelles results in the shorter and stiffer PNIPAM string, which diminishes the monomer interaction, as the above mentioned. But, even if the monomer interaction completely vanishes at a critical extension, or νmonomer ≈ 0, the excluded– volume effect does not accordingly disappear, because the micelle–micelle and monomer–micelle interactions, or νmicelle and νmonomer–micelle, remain in the system unless the pearl–necklace structure is completely disbanded. To elucidate the effect of the monomer interaction on the excluded volume, we first use the excluded volume parameters νeff and νmonomer, respectively, to calculate the brush height. The results are representatively shown in Figure 9a as a function of temperature. When the temperature is higher than ∼ 293 K, which facilitates a continuous growth of the persistence length (Figure 4), the effect of the monomer interaction, or νmonomer, on the brush height dramatically diminishes and eventually becomes negligible. In this situation, even at ψ = 2, the tethered chains are effectively stretched by the repulsive interactions involving the bound micelles.


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Figure 9. (a) Calculated brush height versus temperature at ψ = 2 with comparison to experimental data (empty squares). The solid line is calculated using νeff and the dash line is calculated using

νmonomer. (b) Extension = Re/Lc versus νeff/(ψLp).

With regard to the dependence of the extension on the effective excluded volume parameter, we employ < L >∼ (ν eff /ψLP )− βV to explore the relation between and νeff. This power–law is meaningful because is proportional to Lp but inversely to νeff. It is seen from Figure 9b that the – νeff/(ψLp) data are superposed as two master curves, depending on ψ. When ψ = 2 and 3.7, or under smaller electrostatic forces, scales with νeff/(ψLp) as < L >∼ (ν eff /ψLP ) −0.35 . When ψ = 5.2 and 6.6, or under larger electrostatic forces, the exponent βV is reduced to ∼ 0.2. At ψ = 2, which is the minimum number required to form a pearl–necklace structure, the micelle– constrained PNIPAM string should be fairly flexible because it accommodates the largest number 25 Environment ACS Paragon Plus


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of the monomer corresponding the shortest persistence length (Figure 4a). Accordingly, βV ≈ 0.35 reflects the significant interaction between the monomers within the string. With increasing ψ, the micelle–constrained string becomes increasingly the shorter and stiffer. As such, due to the strong stretch of the segments, βV ≈ 0.2 implies that the contribution of the monomer interaction to the excluded volume is negligible or rather small if anything. All combined together, the force–extension behaviour of the micelle–constrained PNIPAM can be summarised by  ν eff   < L >∼   ψL p   

− βV

 af C     k BT 

−0.6

(12)

This model, which includes three leading factors, i.e., temperature, electrostatic force, and excluded volume, adequately characterizes the intricate force–extension behaviour of the micelle–constrained PNIPAM at interfaces. There is a lack of literature data concerned with the force–extension behaviour of similar systems. It is unclear whether the scaling relations obtained can be incorporated, as an inverse behaviour, into the conceptual framework of the well–known model,50,67,68 because the underlying mechanisms are different from each other. Considering the complexity of stimuli–responsive neutral brushes accommodating charged nanoparticles, the further research is needed to understand the concurrency of the conformational extension and intermolecular force.

4. CONCLUSIONS The thermoresponsive PNIPAM brush–micelle complexes have been investigated below TLCST, experimentally and theoretically, in efforts to characterize the flexibility of micelle–constrained PNIPAM at interfaces. At cSDS < cac, the partially collapsed brush is viewed as coexisting extended and collapsed layers. When the strong stretching of the collapsed layer is accomplished by bound micelles at cSDS > cac, the minimum force required is estimated from the restoring force.


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Using a mean–field model, we perform the data fitting to the experimentally measured height of tethered PNIPAM underpinned by bound micelles. Our investigation draws out the temperature and micelle dependence of persistence length, which is difficult to be experimentally determined, allowing us to quantitatively exam the flexibility of micelle–constrained PNIPAM at interfaces. It is found that the relative persistence length increases with the temperature T and the number of bound micelle per chain ψ. But, the increases in the persistence length results in the decrease in the electrostatic repulsion fC between the bound micelles. The results indicate that the synergistic effect of T and fC on the persistence length per ψ can be approximated by the power–law. The fraction of charge–dependent persistence length is found to scale with the Debye screening length by

L p, e / L p ∼ κ −1.8 , suggesting the bound charges affecting the persistence length are similar to the fixed charges of polyelectrolytes. When viewed from the force–extension, the extension of micelle–constrained PNIPAM decreases with the electrostatic repulsion fC as < L >∼ fC− β F , where βF increases from 0.58 to 0.8 with increasing ψ. The synergistic effect of fC and T on follows a universal power–law < L >∼ ( f C / k BT ) −0.6 , irrespective of ψ. In spite of intricate interplay among the components, the

relation between the extension and the effective excluded volume parameter νeff can be described by < L >∼ (ν eff /ψLP ) − βV , where βV ≈ 0.35 when the monomer interaction is significant and βV ≈ 0.2 when the monomer interaction is weak or negligible. This work is not restricted to the PNIPAM brush–micelle system. The similar strategy can be utilised to study the flexibility of stimuli–responsive brushes which are infiltrated by other inclusions such as colloidal and bio–related particles.

■ AUTHOR INFORMATION Corresponding Author *E-mail: [email protected]; Telephone: 61-0409992360. 27 Environment ACS Paragon Plus


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Notes The authors declare no competing financial interest.

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Synergistic Effects of Bound Micelles and Temperature on the

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