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Surface segregation and bulk aggregation in an athermal thin film of polymer-nanoparticle blends: Strategies of controlling phase behavior Chih-Yu Teng, Yu-Jane Sheng, and Heng-Kwong Tsao Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.6b04681 • Publication Date (Web): 21 Feb 2017 Downloaded from http://pubs.acs.org on February 28, 2017
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Surface segregation and bulk aggregation in an athermal thin film of polymer-nanoparticle
blends:
Strategies
of
controlling
phase
behavior
Chih-Yu Teng,1 Yu-Jane Sheng1,* and Heng-Kwong Tsao2,* 1
Department of Chemical Engineering, National Taiwan University, Taipei, 106, Taiwan 2
Department of Chemical and Materials Engineering, Department of Physics, National Central University, Jhongli,320, Taiwan
Abstracts The phase behavior of an athermal film of a polymer-nanoparticle blend (PNB) driven by depletion attraction is investigated by dissipative particle dynamics for nanospheres and nanocubes. Surface segregation is observed at low nanoparticle concentrations while bulk aggregation is seen at high concentrations. Surface excess and the aggregation number can be controlled by tuning the nanoparticle concentration. As surface-roughened or polymer-grafted nanoparticles are used, uniform PNBs are acquired due to the lack of depletion. Thus, the addition of surface-roughened nanoparticles into PNBs of smooth nanoparticles can be employed to tune the phase characteristics. It is found that bulk aggregation is suppressed for both
polymer-nanosphere
segregation
is
impeded
and for
polymer-nanocube
blends.
polymer-nanosphere
blend
However, but
surface
enhanced
for
polymer-nanocube blend owing to the distinct influence of the nanoparticle shape on depletion.
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I. Introduction Polymer-nanoparticle blend (PNB) is a promising class of materials and its thin film has received great attention in the past few years.1-3 The addition of low amount of nanoparticles into the polymer thin film often results in material properties superior to those of pristine matrix polymers. Moreover, blending nanoparticles with polymer may impart new properties that unfilled matrices do not possess. For example, polymer thin films casted on solid substrates are easily ruptured due to dewetting.4 It was demonstrated that adding fullerene nanoparticles to the unstable polystyrene thin film on a silicon substrate can suppress dewetting.4 Normally nanoparticles have a tendency to aggregate into clusters rather than dispersing in the polymer host due to their immiscibility and depletion attraction.5,6 However, when interfaces are present, it has been observed that nanoparticles migrate to interfaces and a layer of nanoparticles is formed near the substrate.7,8 This has been attributed to ”entropic-push” transition induced by the surfaces.9 Since the location of nanoparticles in the thin film of the polymer affects the properties of PNB, it is important to realize the phase behavior of PNB associated with the distribution of nanoparticles. In an athermal PNB film, it is found theoretically and experimentally that nanoparticles tend to segregate to the interfaces.10-14 This surface segregation is shown to be first-order phase transition based on the density functional theory.9,15 Grafting polymers onto the nanoparticles can suppress the segregation of nanoparticles to the substrate as demonstrated by the study of molecular dynamics.16 In the blend of polystyrene (PS) and PS-grafted gold nanoparticles, it was shown that the degree of surface segregation can be mitigated by controlling the nanoparticle size and the chain lengths of the grafting polymers and host polymers.10-12 Recently, it was reported that the migration of bare nanoparticles to the surface can also be prevented by adding polymer-grafted
nanoparticles.17
The
resulting
spatial
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distribution
of
bare
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nanoparticles is dictated by grafting polymer length and grafting density of the polymer-grafted nanoparticles. The inhibition of surface segregation is attributed to the formation of binary aspherical clusters. In an athermal blend of nanoparticles and polymers, aggregation of nanoparticles is induced purely by attractive depletion.6 The depletion interaction is entropic in nature and dependent on the shape and size of nanoparticles and polymeric volume fraction.5,6 The depletion effect is generally weak for spherical particles but becomes significant for platelet-like particles.18 Moreover, a good dispersion appears for small nanoparticles while clusters are observed for large ones.18 In an athermal thin film of PNB, the interfaces complicate the phase behavior. The depletion interaction is ubiquitous between particle and wall and among particles. As a result, there exists a competition between surface segregation and bulk aggregation of nanoparticles. If the depletion is repressed, a good dispersion of nanoparticles may take place. It is known that the strength of depletion attraction can be manipulated by polymer grafting and surface roughening of the nanoparticles.19,20 In this work, the crossover between surface segregation and bulk aggregation driven by entropic depletion is first explored by dissipative particle dynamics (DPD) simulations for smooth nanospheres and nanocubes. With a variety of shape-controlled synthesis methods, nanostructures of cubes have been synthesized21(a)-(d) and studied.6 Then, suppression of both surface segregation and bulk aggregation by surface roughening or polymer grafting of the nanoparticles is investigated. Finally, the effects on the extent of change in surface segregation and bulk aggregation of smooth nanoparticles by the addition of surface-roughened or polymer-grafted nanoparticles into the polymer-smooth nanoparticles blend are studied.
II. Model and Simulation Methods 3
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Typically, a thin film is a layer of material ranging from fractions of a nanometer to several micrometers in thickness. In this work, the athermal thin film of PNB consists of nanoparticles and polymers confined between two neutral walls separated by a distance of H (Figure 1a). Note that a bounce-back reflection mechanism was adopted for PNB interacting with the wall.22 The simulations were performed at the box size of × × under the two-dimensional (x- and y-) periodic boundary condition. We have set = = = 50 for nanosphere systems and = = = 35 for nanocube systems. If a unit length in our simulation denotes 5 nm, then the thickness of our system is 250 nm. The matrix is linear polymers constructed by 50 DPD bonded beads. The radius of gyration of the matrix polymer is Rg ≈3.48. The nanoparticle can be a nanosphere of radius r=3 or a nanocube of side length l=1.5 (Figure 1b). A nanocube is generated in a body-centered cubic arrangement and a nanosphere is made by removing beads from a nanocube beyond a sphere of radius r. While a spherical nanoparticle consists of 113 DPD beads, a nanocube is composed of 35 beads. Obviously, the polymer size is small compared to the thin film thickness but is larger than nanospheres and nanocubes (r/Rg=0.86 and l/Rg=0.43). In our simulations, the nanoparticle is constructed by an assembly of DPD beads as shown in Figure 1. It is different from the hard particle of the appropriate size in the DPD system, in which more complicated solvent-colloid and colloid-colloid interactions such as Lennard-Jones potentials have to be used.23 The mean density of DPD beads in the system is 3 (i. e. ρ = 3) beads per unit volume and the total number of particles in the system is × × × 3.
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Figure 1. Schematics of the (a) thin film of a nanoparticle-polymer blend (b) linear polymer, nanosphere, and nanocube.
The conservative force between any pair of DPD beads is expressed by a soft-repulsive interaction, = ( ̂ , where represents the maximum
repulsion between beads i and j. and ̂ are the distance and unit vector between the two beads, respectively. All forces vanish beyond the cutoff distance (rc =1). In our athermal system, all the interactions among nanoparticles, polymers, and walls are the same. Consequently, all interaction parameters are simply chosen as 25 to ensure the athermal condition and the occurrence of adsorption cannot be driven by 5
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enthalpic attractions. Note that the DPD system exhibits a compressibility close to that of liquid water as = 25.24 For thermodynamic properties, the boundary models are not relevant as long as are specified.24 Any two adjacent DPD beads in polymer or nanoparticle are linked by the spring force following Hooke’s law, = ̂ , where the spring constant is =100 and the equilibrium
bond length =0.7. The friction coefficient of the dissipative force γ and the noise amplitude of the random force σ are set to be 4.5 and 3. All the units are scaled by the bead mass m, cutoff distance rc, and thermal energy kBT. The equation of motion evolves based on a modified velocity Verlet algorithm with λ = 0.65.24 Each system was equilibrated for at least 106 DPD steps with the time step ∆t=0.04. Proper equilibration is ensured as the distribution of nanoparticles (see Figures 2a and 4a) becomes unchanged. More details can be found elsewhere.25,26 In this work, we deal with as cast films, which are the mixture of polymer melt and nanoparticles. Therefore, nanoparticles are able to migrate through polymer melt (matrix) by thermal fluctuations.
III. Results and Discussion First, we demonstrate that the crossover from surface segregation to bulk aggregation can be achieved by tuning the nanoparticle concentration. Consider the nanosphere-polymer composite and the total volume fraction of nanospheres varies from !" =0.075 to 0.25. Note that !" =
#$#%& '$.$( )*) + %), ($- '%'$,*. - , #$#%& '$.$( )*) + %), ' #. ,,# /
. Since
each DPD bead has the same mass, !" is equivalent to the weight percentage of nanoparticles in the blend frequently used in experiments. The total numbers of nanoparticles in the system are equal to the system volume ( × × ) × the density (3) × the particle volume fraction (!t) / (DPD beads in a nanoparticle). The concentration profiles of nanospheres !0 (1 are shown in Figure 2a and the 6
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corresponding snapshots in Figure 2b. At a low concentration !" =0.075, the local concentration exhibits a maximum near the wall (!/% ∼0.23) but falls to the constant bulk concentration in the center region (!2 ∼0.05). Evidently, surface segregation of nanoparticles in terms of the ratio of !/% /!+ in the thin film appears purely due to the entropic effect.10-12 At a medium concentration !" =0.15, the concentration still displays a maximum near the wall but the uniform concentration region away from the wall is not clear. The local minimum and hump occur and the extent of surface segregation decreases. Those results can be attributed to the formation of small clusters of nanospheres shown in the corresponding snapshot (Figure 2b). It seems that surface segregation and bulk aggregation coexist. At a high concentration !" =0.25, the concentration varies significantly with the position and the bulk concentration cannot be defined. That is, no flat region appears in the middle of the slit for higher !" . It can be realized by the size and shape of the aggregates. When the aggregate size is comparable to the distance between two walls, the excluded volume of the aggregate similar to a hard sphere becomes substantial so that the nanoparticle volume fraction comes to be larger in the central region. This effect will diminish as the separation is increased.
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Figure 2. (a) The variation of the volume fraction of nanospheres with the position for a nanosphere-polymer blend. (b) The corresponding equilibrium snapshots of nanospheres are demonstrated. In order to characterize surface segregation and bulk aggregation quantitatively, surface excess (S*) and weight average aggregation number () in the bulk phase 9
are employed. The surface excess is expressed as S ∗ = 5: 6! (1 !+ 7 81, where H depicts the film thickness. For simplicity, !2 is defined as the mean concentration in the center (bulk) region, 0.2
