Mesoscopic Simulations of Adsorption and Association of PEO-PPO

Oct 20, 2016 - Department of Mechanical and Electrical Engineering, Dazhou Vocational and Technical College, Dazhou, Sichuan 635000, P. R. China. ‡ ...
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Mesoscopic Simulations of Adsorption and Association of PEO-PPOPEO Triblock Copolymers on a Hydrophobic Surface: From Mushroom Hemisphere to Rectangle Brush Xianyu Song,*,† Shuangliang Zhao,‡ Shenwen Fang,§,∥ Yongzhang Ma,⊥ and Ming Duan§,∥ †

Department of Mechanical and Electrical Engineering, Dazhou Vocational and Technical College, Dazhou, Sichuan 635000, P. R. China ‡ State Key Laboratory of Chemical Engineering, East China University of Science and Technology, Shanghai 200237, P. R. China § College of Chemistry and Chemical Engineering, Southwest Petroleum University, Chengdu 610500, P. R. China ∥ Oil & Gas Field Applied Chemistry Key Laboratory of Sichuan Province, Chengdu 610500, P. R. China ⊥ Sichuan Province Academy of Industrial Environmental Monitoring, Chengdu 610500, P. R. China S Supporting Information *

ABSTRACT: The dissipative particle dynamics (DPD) method is used to investigate the adsorption behavior of PEO-PPO-PEO triblock copolymers at the liquid/solid interface. The effect of molecular architecture on the selfassembled monolayer adsorption of PEO-PPO-PEO triblock copolymers on hydrophobic surfaces is elucidated by the adsorption process, film properties, and adsorption morphologies. The adsorption thicknesses on hydrophobic surfaces and the diffusion coefficient as well as the aggregation number of Pluronic copolymers in aqueous solution observed in our simulations agree well with previous experimental and numerical observations. The radial distribution function revealed that the ability of self-assembly on hydrophobic surfaces is P123 > P84 > L64 > P105 > F127, which increased with the EO ratio of the Pluronic copolymers. Moreover, the shape parameter and the degree of anisotropy increase with increasing molecular weight and mole ratio of PO of the Pluronic copolymers. Depending on the conformation of different Pluronic copolymers, the morphology transition of three regimes on hydrophobic surfaces is present: mushroom or hemisphere, progressively semiellipsoid, and rectangle brush regimes induced by decreasing molecular weight and mole ratio of EO of Pluronic copolymers.

1. INTRODUCTION

from aqueous solutions to a hydrophobic surface. Lee and coworkers8 investigated the adsorption behavior of the PEOPPO-PEO triblock copolymers on a poly(dimethylsiloxane) (PDMS) surface, and the feasibility of using the copolymer as an additive for the aqueous lubrication of an elastic sliding contact was also examined. The association of Pluronic copolymers adsorbed from aqueous solutions onto polypropylene (PP), polyethylene (PE), and cellulose surfaces was also studied by Li et al.9 using atomic force microscopy (AFM). They found that the hydrophobic polyolefin surfaces were smoothed by the adsorbed PEO-PPO-PEO triblock copolymers, whereas more sharpened morphologies were observed on the hydrophilic cellulose surfaces. The film morphologies after the absorption of PEO-PPO-PEO triblock copolymers depend on the hydrophobicity and the roughness of substrate surfaces. Compared to hydrophilic surfaces, there are strong interactions between PEO-PPO-PEO triblock copolymers and hydrophobic

Poly(ethylene oxide)-poly(propylene oxide)-poly(ethylene oxide) (PEO-PPO-PEO) constitutes a group of amphiphilic block copolymers, often known as Pluronic (BASF Co.), which has received increasing attention as a modifier of solid surfaces through physical adsorption.1,2 This is mainly due to their amphiphilic properties that endow molecular structures with tailorable surface affinities, depending on the adsorbing surfaces and the surrounding medium. These materials are of great interest because they not only deliver steric stabilization in solid dispersions and generate controlled surface structures upon arrangement of materials but also modify interfacial properties such as wetting and lubrication.3,4 They also can be used on nanoparticles as surface coatings5 and even as drug-delivery vehicles upon which the drugs can be solubilized and transported in solution.6 The interfacial behaviors of Pluronic copolymer solutions in the presence of solid surfaces, both mineral and polymeric, have been investigated by a number of authors. For example, by using surface plasmon resonance (SPR), Green and coworkers7 reported the adsorption of Pluronic copolymers © 2016 American Chemical Society

Received: June 29, 2016 Revised: October 20, 2016 Published: October 20, 2016 11375

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Langmuir surfaces.2,6,10 Elisseevael at.11 studied the influence of NaCl on the adsorption behavior of PEO-PPO-PEO triblock copolymers on an aqueous silica interface. Further understanding of the interfacial behaviors and selfassembly processes is necessitated; however, such endeavors are often limited by the availability of fine experimental techniques. Fortunately, various simulation methods, such as Monte Carlo simulation (MC),12 molecular dynamics (MD),13 and dissipative particle dynamics (DPD),14−16 are available to solve these problems. It is in principle viable to study the adsorption of polymer molecules at the atomistic level by using molecular dynamics (MD).17 MD can provide specific information regarding the interfacial behavior of PEO-PPO-PEO triblock copolymers at hydrophobic surfaces without compromising the atomistic details. However, the time scale and length scale accessible to classical MD is too short to allow for observing the adsorption behavior and film morphologies at hydrophobic surfaces. The dissipative particle dynamics (DPD) is a widely used mesoscale technology and it can deal with a much larger system with a longer simulation time than can MD. On one hand, DPD provides an ideal tool for studying and understanding the various kinds surfactant systems, including the surfactants/oil/water interface,16 self-assembly of surfactants in aqueous solution,17 and drug loading/releasing processes.18 On the other hand, because of the introduction of dissipative force and the coup of friction coefficient and noise amplitude, DPD proves to be an excellent methodical method for the simulation of coarse-grained systems over long length and time scales. The purpose of this study is to investigate the influence of molecular architecture on the self-assembled monolayer adsorption of PEO-PPO-PEO triblock copolymers on a hydrophobic surface. Green et al. have previously reported PEO-PPO-PEO adsorption on a planar hydrophobic surface.7 They highlighted important qualitative trends, notably, the relative impact of the PPO and PEO blocks on the adsorbed amount at equilibrium and the greater rates of adsorption for micellar solutions over nonmicellar solutions for copolymers that have a higher content of PPO over PEO. Most of the aforementioned studies have addressed the influence of molecular architecture on the adsorption of PEO-PPO-PEO triblock copolymers on liquid/solid interfaces, and only a few molecular dynamics simulations have paid attention to the adsorption dynamics.19−22 For example, Malmstenel et al.20 studied the adsorption of block copolymers of types PEO-PPOPEO and PEO. Their experimental findings were analyzed with a modified mean-field theory. Unfortunately, the influence of molecular architecture on the self-assembled monolayer film structure of PEO-PPO-PEO triblock copolymers on hydrophobic surfaces is still poorly understood, and this is probably because DPD simulation relies on interaction parameters between different components and these parameters are difficult to obtain. In this work, we employ the DPD method to investigate the influences of molecular architecture on adsorption behavior and film morphologies of PEO-PPO-PEO triblock copolymers on a hydrophobic surface. The DPD approach allows us to probe macroscopic phenomena such as self-assembly, adsorption, and self-organization of the surfactants at reasonable length and time scales with affordable computational effort. The adsorption behavior and film morphologies of PEO-PPOPEO triblock copolymers at the liquid/solid interface are investigated by accessing the adsorption process, film properties, and adsorption morphologies.

2. METHODOLOGY 2.1. DPD Method. Dissipative particle dynamics (DPD), as a stochastic simulation technique, was introduced by Hoogerbrugge23 and Koelman.24 DPD often is used to simulate dynamic behaviors of complex fluids. In DPD, several molecules of the same type are grouped into a single coarsegrained bead. Every bead’s motion is governed by Newton’s equations of motion24 ∂ri ∂vi f = vi; = i ∂t ∂t m

(1)

where ri and vi are the position vector and velocity of the ith bead, respectively. In general, the force exerted on the ith bead; namely, fi, can be written as25 fi =

∑ (FCij + FijD + FijR ) + f Si + f iA (2)

i≠j

The terms in parentheses are three nonbonded forces acting between a pair of beads, and they are conservative repulsive forces (FCij ) representing excluded volume, dissipative forces (FDij ) representing viscous drag, and random forces (FRij ) representing the stochastic impulse. The remaining terms are forces due to bonded interactions: the spring force (fSi ) and angle force (fAi ).The sum in eq 2 runs over all of the other particles with a cutoff, rc, that is set as the length scale parameter of the system and thus equals 1. Apparently, all forces between beads i and j vanish when the distance is beyond rc.25 The conservative repulsive force usually follows24 FCij = αijω(rij)eij

(3)

where αij = αji > 0, indicating that this force is always repulsive, rij is the distance between beads i and j, and eij is the unit vector (ri − rj)/rij. The function ω(r) determines the radial dependence of the force; the function is continuous, positive for r < rc and zero for r ≥ rc. DPD uses a simple linear weight function for the conservative force: ωC(r)) = 1 − (r/rc) for r < rc.25 FDij is a dissipative or frictional force, and it is proportional to the velocity with which two beads approach each other. FRij is a random force26 FijD = −γωD(rij)(vij·eij)eij

(4)

1 eij Δt

(5)

FijR = σijωR (rij)ξij

where ωD and ωR are r-dependent weight functions that ensure that FRij and FDij vanish when rij becomes greater than rc, γ is the friction factor or the amplitude of the dissipative force, and σ defines the fluctuation amplitude of the random force or noise parameter. Here vij is defined as vij = vi − vj, the velocity difference in two beads, and Δt is the time step with which the equations of motion (eq 1) are solved. Parameter ξij in eq 5 is a randomly fluctuating variable with a Gaussian statistics white noise term with zero mean ⟨ξij(t)⟩ = 0 and unit variance.26 To obey the fluctuation−dissipation theorem, it must have ωD = (ωR)2, and the system temperature is determined from the relation between γ and σ, namely, σ2/γ = 2kT. The same integration algorithm, weight functions, and parameters as Groot and Warren used are utilized throughout the article:27 11376

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Figure 1. Morphology of structures formed from aqueous 10% Pluronic copolymers solutions at 15 ns: (A) F127, (B) P105, (C) P123, (D) P84, and (E) L64. The water beads are suppressed for clarity. PO is indicated with light blue color, and EO is in yellow (the color representations remain the same below).

ω(r ) = ωC(r ) = ωD(r ) =

ωR (r )

where X and Y refer to the numbers of EO and PO monomers, respectively, and x and y are the corresponding numbers of coarse-graining beads in topology. On the basis of this relationship, the coarse-grained topologies for F127, P105, P123, P84, and L64 are constructed and listed in Table S1 in the Supporting Information (SI). From Table S1, these Pluronic copolymers that have different molecular weights and mole ratios of EO are chosen. Regarding the molecular weight, we have F127 > P105 > P123 > P84 > L64. Concerning the mole ratio of EO, we have F127 > P105 > P84 > L64 > P123. The length scale rc in angstroms, mass scale m, and time scale τ in picoseconds can be evaluated as rc = 3.107(ρNm)1/3 Å, m = Nmmwater amu, and τ = (1.41 ± 0.1)Nm5/3 ps,30,34 where ρ = 3 is the DPD number density and mwater is the mass of the water molecule. 2.3. DPD Parameters and Simulation Details. The results of DPD simulations are usually determined by two parameters: the mode for coarse-grained molecules and the interactions of DPD particles. The bead−bead interaction parameters are determined by the following equation:36

(6)

Throughout this article, reduced units are used. Specifically, rc is the unit of length, kBT (the temperature of the thermostat) is the unit of energy, and the mass unit is the mass of a DPD bead. In these units, the dissipative parameter is γ = 4.5, and the noise parameter is σ = 3.0.28 All DPD beads in the same chemical molecule are connected by a loosely bounded spring. By means of this spring force (fS), the molecule’s stiffness can be controlled, and the beads can be interconnected to complex topologies. The spring force experienced by bead i is fSi = −∂US/∂ri US =

∑ b

1 Cb(rb − r0)2 2

(7) 29

S

where U is the total bonded potential, r0 is the equilibrium bond length, and Cb is the bond spring constant. An angular force (fA) also acts among three connected beads. By means of this angular force, the beads can be interconnected to specific conformations of the mesomolecules. The force experienced by bead i due to angular interactions is fA = −∂UA/ ∂ri, where UA is the total angular potential29 A

U =

∑ aα

1 ka(θα − θα0)2 2

aij = aii + 3.497χij

The values of χij can be calculated from the solubility parameters or determined from MD simulations. The interaction parameters in our simulation system including that for mimicking the hydrophobic surface are given in Table S2 on the basis of the previous assumptions and using values provided in previous publications.37,38 The parameters for bond lengths and bending angles are listed in Table S3, and they are extracted from the reference.39 These parameters were obtained from explicit solvent (AES) MD simulations by inverting the Boltzmann method, and they had been adopted for simulations on the self-assembly behaviors of Pluronic copolymers in aqueous solution, giving rise to comparable predictions with experimental results.

(8)

θ0a

is the equilibrium value for angle α and kα is the stiffness parameter. The parameters of the spring force and angular force will be discussed in section 2.3. 2.2. Coarse-Graining Method. In our work, three water molecules are grouped as one DPD bead, and this grouping has already been confirmed to produce ideal surfactants systems.30,31The coarse-graining of the polymer required for the DPD simulations is done as described by van Vlimmeren et al.32 The relationship between the atomistic chains and Gaussian chains for Pluronics is given as33 X /x = 4.3; Y /y = 4.3

(10)

(9) 11377

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Figure 2. Morphology of structures as a function of time formed from aqueous 15% P84. The corresponding times from the upper left to the lower right in each subfigure are 0.12, 0.42, 1.21, 1.75, 1.99, and 4.83 ns. The water beads are suppressed for clarity (The color representations are the same as in Figure 1.)

formed from aqueous 15% Pluronic copolymer solutions is presented in Figure S1 in the SI. To investigate the effect of molecular architecture on the self-assembled monolayer adsorption of Pluronic copolymers on hydrophobic surfaces, the adsorption dynamics, density profile, film thickness, radius of gyration, radial distribution function, order parameter, shape parameter, and degree of anisotropy are accessed and discussed below. 3.1.2. Adsorption Processes. Snapshots of the P84 system in contact with the hydrophobic surface are presented in Figure 2. From the initial random configuration, Pluronic copolymers began coating the hydrophobic surfaces (Figure 2A,B). Simultaneously, they started self-assembling in the water away from the surfaces. The initial coating was fast because the surface was uncoated, and the adsorption rate decreased gradually as the surfaces became coated. This is expected because the surface becomes increasingly unavailable for adsorption with time. However, the self-assembly in aqueous solution becomes predominant once the hydrophobic surface is fully coated. Some similar adsorption phenomena were observed in block copolymers such as C12E3, C12E5, and C12E8 (E represents an ethylene glycol unit).40 We also find the formation of larger micelles by reassembling two smaller micelles (Figure 2D,E). This also reveals that these Pluronic copolymers are capable of forming micelles in bulk water by spontaneous self-assembly. In the process of random motion, this micelle diffused toward one of the hydrophobic surfaces. All of the trends in P84 observed in snapshots were similar to those for other Pluronic copolymers, and more detail information can be found in avi video files of Pluronic copolymers in the Supporting Information (SI). We also simulated the self-organization of Pluronic copolymers on hydrophobic surfaces at 25% concentration, as shown in Figure S2 in the SI. From Figure S2A, we find that the adsorption morphology formed from an aqueous 25% P123 Pluronic copolymer solution was more intensive than those formed from 10 and 15% P123 Pluronic copolymer solutions. Moreover, the adsorbed area of P123 Pluronic copolymers at 25% concentration was larger than those at 10 and 15% concentrations, and this indicates that the 25% concentration is close to the saturated adsorption concentration. The density fields of structures formed from aqueous 25% P123 Pluronic

The DPD simulations were carried out in an NVT ensemble using the Mesocite module embedded in the Materials Studio 7.0 package.26,36 In our work, all simulations were accomplished in a cubic box with a size of (100 × 120 × 100)rc3 with periodic boundary conditions applied in three directions. The systems of periodic boundary conditions are considered to be surrounded on all sides by replicas of themselves, forming an infinite macrolattice. Periodic boundary conditions are used in DPD simulations to avoid problems with boundary effects caused by finite size, and they make the system more like an infinite one. The system temperature is set at 298 K. All particles of the solid surface located at the bottom of the simulation box were fixed at their balanced positions. The thickness of solid surfaces is 10.0rc. Different from the density of entire fluid system in which the reduced density is ρ = 3.0, the bead density of solid surfaces is set as 2.5ρ in order to make a distinction of solid substrates. The enclosed simulation cell is composed of 15, 20, or 25% concentration Pluronic copolymers in aqueous solution. The polymer concentration is described by the number ratio of polymer beads to total beads, with φ denoting the total polymer concentration and φi denoting the concentration of each species (i = 64, 84, 105, 123, or 127). A total of 10 × 105 DPD simulation steps were carried out with a Δt = 0.005 time step. The scales used in DPD units were as follows: length scale, 6.46 Å; mass scale, 54 amu; energy scale, 0.59191 kcal/ mol; and time scale, 3.0158 ps. The total real dynamic time is ttotal = NstepsΔtτtime scale, namely, 15.08 ns.

3. RESULTS AND DISCUSSION 3.1. Adsorption Process. 3.1.1. Adsorption Morphologies. In this article, we focused on the influence of molecular architecture on the adsorption of PEO-PPO-PEO triblock copolymers on hydrophobic surfaces. We studied the selfassembly and self-organization of Pluronic copolymers of F127, P105, P123, P84, and L64 at a concentration of 10, 15, or 25%. The morphology of the structures formed from aqueous 10% Pluronic copolymer solutions at 15 ns is presented in Figure 1. Obviously, the molecular architecture of Pluronic copolymers made a strong impact on the adsorption morphologies. As can be seen in Figure 1, hydrophobic block PPO adsorbed onto the hydrophobic surfaces whereas hydrophilic block PEO freely stretched in aqueous solution. The morphology of structures 11378

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Langmuir copolymers are given in Figure S2B,C. From the side-view structure of the density field, we can see that changes in phase separation occur in the adsorption process. Adsorbed P123 on the hydrophobic surfaces is separated into two layers: the first layer, composed of PO, is adsorbed on the hydrophobic surfaces; the second layer, consisting of EO, covers the PO layer. The aggregation number is an important quantity, and it characterizes the packing degree of micelles in aqueous solution. The aggregation numbers of Pluronic copolymers in aqueous solution were calculated. The aggregation number of Pluronic copolymers is the number of molecules that associate to form a micelle. The aggregation number of F127 in our simulation is 14.2, which compares well with the reported value of 15.0 at the same temperature.41 For L64, Almgren et al.42 calculated the aggregation number based on static light scattering, and they found it to be 4 at a slightly different temperature (299 K).The present study predicts 5.12, which is close to the experimental value. 3.1.3. Adsorption Dynamics. To study the Pluronic copolymer adsorption mechanism onto the hydrophobic surface in more detail, the adsorption dynamics were studied. Figure 3 shows the weight mass of Pluronic copolymers

Figure 4. Morphology of structures as a function of time formed from aqueous 15% P105. The corresponding times from the upper left to the lower right in each subfigure are 10.37, 10.68, 10.92, and 11.16 ns. The water beads are suppressed for clarity.

phenomenon of Pluronic copolymers on surfaces is a feeding mechanism.40 The PO segments of Pluronic copolymers near the surfaces interacted with those of the surfactants already adsorbed on hydrophobic surfaces. At this point, we find that the single molecular or bimolecule and micelle start feeding the hydrophobic surfaces in stages I and II; afterward, the available surface area becomes smaller and the adsorption of Pluronic copolymers onto the surface becomes more difficult. To compare the adsorption ability of Pluronic copolymers onto the surface, the diffusion coefficients are also examined. The diffusion coefficients D of Pluronic copolymers are calculated by fitting the slopes of the mean square displacements (MSD) that are shown in Figure S3 of the SI. In Table S4 of the SI, we collect the diffusion coefficients from our simulation: F127, 3.22 × 10−10 m2/s; P105, 5.57 × 10−10 m2/s; P123, 2.14 × 10−10 m2/s; P84, 3.51 × 10−10 m2/s; and L64, 5.13 × 10−10 m2/s at 10% concentration. These values agree well with the reported results.19 As Figure 3 shows, there is a positive correlation between the duration time for complete adsorption and the diffusion coefficient of Pluronic copolymers. For example, the P123 needs the shortest time to reach complete adsorption at both concentrations of 10 and 15%, and its diffusion coefficient is the smallest and reaches 2.14 × 10−10 and 2.69 × 10−10 m2/s at both concentrations. The positive correlation can be explained by the fact that the diffusion coefficient of Pluronic copolymers is smaller if its attraction with the hydrophobic surfaces is stronger. According to the adsorption dynamics curves, we find that the adsorption of Pluronic copolymer micelles on the hydrophobic surface gives rise to a sudden jump in the adsorption kinetics during stages II and III. Figure 4 shows the process of Pluronic copolymer micelles being adsorbed onto the hydrophobic surface. As illustrated in Figure 4, the Pluronic copolymer micelle gradually approaches the hydrophobic surface mainly induced by the attractive interaction between the PEO blocks of Pluronic copolymers and the surface, and

Figure 3. Adsorption dynamics as a function of simulation time for (A) 10 and (B) 15% Pluronic copolymer solutions.

adsorbed on the hydrophobic surface as a function of time. Simulations reveal that the initial rapid adsorption was followed by a slow reorganization for a long time. There are three stages in the adsorption process: (1) stage I, single-molecular or bimolecular Pluronic copolymers quickly adsorbed onto the hydrophobic surfaces before 1.0 or 1.5 ns (Figure 2A,B); (2) stage II, one of the micelles formed in aqueous solution reached the vicinity of the surface, so a sudden jump in the adsorption kinetics was observed (Figure 4); (3) stage III, after 4.0 or 4.2 ns, a larger micelle formed and finally adsorbed onto the hydrophobic surfaces. Overall, stage III took place over a longer time than for stage II and stage I because the adsorption 11379

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Figure 5. Density profiles along the Y-axis direction: (A) F127, (B) P105, (C) P123, (D) P84, and (E) L64 at 15% concentration.

1.5−3.8 nm, in good agreement with previous experimental and numerical observations.20 Besides, the film thickness curves of different Pluronic copolymers decrease with decreasing molecular weight. The higher the concentration of Pluronic copolymers in aqueous solutions, the greater the film thicknesses. These results can be confirmed by Figure 1 and Figure S1 in the SI. 3.2.3. Radius of Gyration (Rg). To gain more insight into the effect of molecular architecture on the adsorption of Pluronic copolymers onto hydrophobic surfaces, the radius of gyration Rg was considered. The radius of gyration Rg describes the degree of stretching. It can be calculated using the following equation28

then, the Pluronic copolymer micelle dissolves and melts into the sea of Pluronic copolymers on the surface. 3.2. Film Properties. 3.2.1. Density Profile. One way of characterizing the structure of the Pluronic copolymers/solid/ liquid system is to calculate the density distribution of the different groups, i.e., water, hydrophilic groups (EO), and hydrophobic groups (PO) of each triblock nonionic polymers molecule as a function of a coordinate perpendicular to the interface (called the Y direction). Typical density profiles for the Pluronic copolymers/solid/liquid systems are shown in Figure 5. The density profile is obtained by dividing the volume into 200 bins parallel to the bilayer surfaces. As illustrated in Figure 5, the density profiles of Pluronic copolymers is well described by the morphology of structures of Pluronic copolymers adsorbed on the hydrophobic surfaces (Figure 1). 3.2.2. Interfacial Thickness. Interfacial thickness is an important interfacial physical property that provides a quantitative measure of the volume of the interfacial zone. According to the density profiles, the interfacial thickness is calculated by following the 90−10 criterion. This criterion defines the thickness as the distance along the interface over which the densities of surfactants drop from 90% to 10% of their bulk values.43 The film thickness of different Pluronic copolymers is shown in Figure 6A; the Pluronic copolymers form thin adsorbed layers, with adsorption thicknesses of about

Rg2 =

1 N

N

∑ ( ri ⃗ − rcm⃗ )2 ; i=1

rcm ⃗ =

1 N

N

∑ ri ⃗ i=1

(11)

where ri⃗ denotes the vector for a whole copolymer molecule. The radius of gyration Rg as a function of simulation time for 15% different Pluronic copolymers solutions is shown in Figure 6B. The radii of gyration of different Pluronic copolymers increase dramatically and then reach equilibrium rapidly. From Figure 6B, we find the molecular architecture to be a remarkable influence on the radius of gyration of Pluronic copolymers adsorbed on the hydrophobic surfaces. As Figure 11380

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Figure 7. Radial distribution functions of different structures of (A) 10 and (B) 15% Pluronic copolymer solutions.

Moreover, the g(r) for P123 also exhibits a peak at 0.6 nm. A higher peak indicates a stronger ability to self-assemble. We find that the ability to self-assemble on hydrophobic surfaces is ranked as P123 > P84 > L64 > P105 > F127, proportional to the EO ratio of the Pluronic copolymers. 3.3. Characterization of Adsorption Morphologies. 3.3.1. Order Parameter. In dynamic simulation processes, the order parameter can be monitored to indicate the structural change and can thus yield characteristics of the phase separation and compressibility. The order parameter (P), which is the mean squared deviation from homogeneity for a particular species (A) in volume V, is defined as37

Figure 6. (A) Film thickness of different Pluronic copolymers, (B) radius of gyration as a function of simulation time for a 15% difference in Pluronic copolymer solution concentrations, and (C) radius of gyration of different structures of Pluronic copolymer solutions. The error deviation in the film thickness is calculated by the deviation in the mean value of the film thickness.

PA = ⟨(ηA − ηA0)2 ⟩

6C indicates, the higher the molecular weight of the Pluronic copolymers, the larger the radius of gyration Rg. Moreover, there is a power law relationship between the radius of gyration Rg and molecular weight,44 as shown in the illustration in Figure 6C. 3.2.4. Radial Distribution Function (RDF). The radial distribution function is computed for all pairs of beads or centroids with a distance less than the cutoff value. Radial distribution function can be calculated by using the following equation45 gij(r ) =

where is the overall volume fraction of species A and ηA is the local volume fraction of species A. Note that both quantities are dimensionless in DPD units. Therefore, small values of PA indicate a homogeneous system, and large values suggest strong phase separation. The order parameters of Pluronic copolymers calculated from eq 13 as a function of the simulation time for the 15% concentrations are given in Figure 8. The trend is similar to that in Figure 3 but with transitions at different simulation times, though they are not obvious. The increasing order parameter of Pluronic copolymers along with time indicates that the phase separation gets stronger and the morphology structures of Pluronic copolymers on hydrophobic surfaces are more regular. We find that the order parameter of EO is higher than that of PO but lower than that of water, suggesting that the PO segments are more regular. These results can be seen from the morphology structures and adsorption dynamics in Figure 1. Moreover, the three stage changes of order parameters are well described by the adsorption dynamics (Figure 3). 3.3.2. Shape Parameter and Degree of Anisotropy. To characterize the spherical shape of Pluronic copolymers at the

{ΔNij(r → r + Δr )}V 4πr 2ΔrNN i j

(13)

η0A

(12)

where {ΔNij(r → r + Δr)} is the ensemble-averaged bead number of type j around a bead of type i within the distance from r to r + Δr. V is the system volume, and Ni and Nj are the total bead numbers of types i and j, respectively. The radial distribution function of different structures of Pluronic copolymer solutions at 10 and15% concentrations are shown in Figure 7. A sharp peak can be observed at approximately 0.6 nm for Pluronic copolymers. This implies a strong self-assembly ability among Pluronic copolymers. 11381

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Figure 8. Order parameter as a function of simulation time for 15% Pluronic copolymer solutions: (A) F127, (B) P105, (C) P123, (D) P84, and (E) L64.

anisotropy Δ, the larger Δ is, the further the polymer deviates from sphericity. According to eqs 15 and 16, the shape parameter S and the degree of anisotropy Δ are calculated and shown in Figure 9. F127, P105, and P123 have a smaller shape parameter S and degree of anisotropy Δ, indicating that the morphologies of hemimicelles adsorbed on hydrophobic surfaces are more sharpened. However, P84 and L64 have larger shape parameters S and larger degrees of anisotropy Δ, which range from 0.16 to 0.35 and from 0.23 to 0.32, respectively, showing the formation of the flat hemimicelle morphologies on the hydrophobic surfaces. Also, we find that the film of Pluronic copolymers with a higher EO ratio tends to have standard spherical morphologies on the hydrophobic surfaces. However, the film of Pluronic copolymers with a lower EO ratio shows prolate ellipsoid morphologies on the hydrophobic surfaces. The shape parameter S and the degree of anisotropy Δ of Pluronic copolymers solutions at 25% concentration are shown in Figure S4 of the SI. Similar trends in the shape parameter and degree of anisotropy were observed at 25% concentration. Though different concentrations of Pluronic copolymers were simulated, the concentrations of Pluronic copolymers have little impact on the self-assembly structure, as can be confirmed by the shape parameter (Figures 9 and S4). As the effect of molecular weight on adsorption behavior, we take P84 (Mw = 4200 g/mol, the mole ratio of EO is 43.48%)

solid/liquid interface, shape parameters, the degree of anisotropy, and the shape tension are introduced. For the shape tension, it can be calculated by46 1 Tαβ = N

N

∑ (ai − acm)(bi − bcm) i=1

(14)

where a and b represent x, y, or z components of the bead’s coordinates, respectively. Here, N is the total number of beads in an aggregate, (xi, yi, zi) is the position of the ith bead, and (xcm, ycm, zcm) is the coordinate of the center of mass of the aggregate. The eigenvalues of Tαβ, denoted as λi, are the squares of the three principal radii of gyration, and thus Rg = Tr(T) = Σ3i=1λi. Let λ̅ = Tr(T)/3, and then the shape parameter S and the degree of anisotropy Δ are as follows:47,48 3

S = 27

∏i = 1 (λi − λ ̅ )2 Tr(T )3

(15)

3

Δ=

3[∑i = 1 (λ i − λ ̅ )2 ] 2Tr(T )2

(16)

If S is positive, then the polymer is typically prolate ellipsoid; if S is 0, then the polymer is standardly spherical. If S is negative, then the polymer is oblate ellipsoid. For the degree of 11382

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hydrophobic surface by using atomic force microscopy, as shown in Figure 9C,D. From the atomic force microscopy results, we find that P105 forms a multilayered, inhomogeneous distribution self-assembled film on hydrophobic surfaces. However, P103, which has a lower EO ratio compared to that of P105, shows a smooth and uniform film on hydrophobic surfaces. All of these similar results can also be found from Figures 1 and S1. To investigate the effect of molecular architecture on the hemimicelle morphologies on hydrophobic surfaces, a schematic illustration of the buoy−anchor−buoy (B−A−B) model for self-assembled structures on hydrophobic surfaces is given in Figure 10. Many investigators used a so-called B−A−B model to describe the adsorption of Pluronic copolymers on hydrophobic surfaces, which is derived from an earlier wetting model.9,49 In the B−A−B model, the hydrophobic PPO blocks are expected to strongly bind to the substrate, whereas the hydrophilic PEO blocks dangle in the aqueous solution from the surfaces, forming a free brush layer. Here we present a new B−A−B model for the self-assembled structures induced by different molecular weights and mole ratios of PO of the Pluronic copolymers on the hydrophobic surfaces. As shown in Figure 10, three regimes are present, depending on the conformation of different Pluronic copolymers: mushroom or hemisphere, progressively semiellipsoid, and rectangle brush regimes. The transition among the three regimes is induced by decreasing the molecular weight and mole ratio of EO of the Pluronic copolymers. The radius of the hemisphere RF ranges from 5.8 to 6.4 nm, the radius of the semiellipsoid RF ranges from 4.8 to 5.1 nm, and the thickness L of the rectangle brush is approximately equal to the film thickness of Pluronic copolymers on the hydrophobic surfaces, which ranges from 1.4 to 2.5 nm. Interestingly, the structural transition of Pluronic copolymer films on a hydrophilic surface as a function of polymer concentration was also observed by X-ray reflectivity and atomic force microscopy: from the core−shell structure to the lamellar structure.50 Correspondingly, Pluronic copolymers have enormous potential for use as a modifier of solid surfaces.

Figure 9. (A) Shape parameter and (B) degree of anisotropy of 10 and 15% Pluronic copolymers solutions, and atomic force microscopy image of (C) P105 (EO37PO56EO37) and (D) P103(EO17PO60EO17) on a self-assembled hydrophobic surface.19

and L64 (Mw = 2900 g/mol, the mole ratio of EO is 40%), for example: though P84 and L64 have similar mole ratios of EO, their molecular weights are different. Moreover, the higher mole ratio of EO would results in prolate ellipsoid or rectangle brush morphologies on hydrophobic surfaces as revealed by the shape parameter. We take P105 (Mw = 6500 g/mol, the mole ratio of EO is 50%) and P123 (Mw = 5750 g/mol, the mole ratio of EO is 32.26%), for example, to study the effect of the mole ratio of EO on adsorption behavior. The lower ratio of EO would lead to the formation of more prolate ellipsoid morphologies on hydrophobic surfaces (Figures 1 and S1). Correspondingly, both a lower molecular weight and a lower mole ratio of EO trends toward prolate ellipsoid or rectangle brush morphologies on hydrophobic surfaces. Brandaniet et al.19 investigated the self-assembled film of P105 and P103 on a

4. CONCLUSIONS In this work, the effect of molecular architecture on the adsorption of Pluronic copolymers on a hydrophobic surface is investigated by using dissipative particle dynamics (DPD) simulation. The adsorption dynamics demonstrate that there exist three stages during the adsorption process: (1) in stage I, single-molecular or bimolecular Pluronic copolymers are quickly adsorbed onto the hydrophobic surfaces; (2) in stages II and III, a sudden jump in the adsorption kinetics can be

Figure 10. Schematic illustration of the buoy−anchor−buoy model for self-assembled structures formed by Pluronic copolymers on a hydrophobic surface. RF is the radius of hemisphere hemimicelles of Pluronic copolymers adsorbed on hydrophobic surfaces, and L is the film thickness of Pluronic copolymers on hydrophobic surfaces. 11383

DOI: 10.1021/acs.langmuir.6b02414 Langmuir 2016, 32, 11375−11385

Langmuir

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observed, and this slower adsorption process is dominated by the micelle adsorption. Moreover, there is a linear relationship between the radius of gyration Rg and the molecular weight. According to the radial distribution function, it can be found that the ability of self-assembly on the hydrophobic surface increases with the EO ratio of Pluronic copolymers. The molecular weight and mole ratio of PO of the Pluronic copolymers have unique influences on the morphology of structures formed on the hydrophobic surfaces. The Pluronic copolymers with higher molecular weights and higher mole ratios of PO form more sharpened morphologies of hemimicelles on the hydrophobic surfaces. Depending on the conformation of different Pluronic copolymers, the hemimicelles’ transition model of three regimes on the hydrophobic surfaces is proposed: mushroom or hemisphere, progressively semiellipsoid, and rectangle brush regimes induced by increasing the molecular weight and mole ratio of PO of the Pluronic copolymers.

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ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.langmuir.6b02414. Morphology of structures formed from aqueous 15% Pluronic copolymer solutions; calculation method for the diffusion coefficient; shape parameter and degree of anisotropy of 25% Pluronic copolymers solutions; properties of PEO-PPO-PEO triblock copolymers; and parameters of the conservative force (PDF) Video file for F127, P105, L64, and the simulated systems that contain 15% Pluronic copolymers (AVI) Video file for F127, P105, L64, and the simulated systems that contain 15% Pluronic copolymers (AVI) Video file for F127, P105, L64, and the simulated systems that contain 15% Pluronic copolymers (AVI)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Present Address

(X.S.) College of Chemistry and Chemical Engineering, Southwest Petroleum University, Chengdu 610500, P. R. China. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work is supported by the National Key Basic Research Program of China (2014CB748500), the National Natural Science Foundation of China (91434110), the Blue Fire Project from the National Department of Education (2014-LHJHHSZX-015), and the Fundamental Research Funds for the Central Universities of China. S.Z. also acknowledges the support of the Fok Ying Tong Education Foundation (151069), the Program for New Century Excellent Talents in University (NCET-13-0983), the National Natural Science Foundation of China (project no. 21376193), and the Sichuan Youth Science & Technology Foundation for Innovation Team (2015TD0007). 11384

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