Molecular Dynamics Simulations of Poly(ethylene oxide) Grafted onto

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Molecular dynamics simulations of poly(ethylene oxide) grafted onto silica immersed in melt of homopolymers Zuzana Benková, and M. Natalia Dias Soeiro Cordeiro Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.5b01890 • Publication Date (Web): 14 Aug 2015 Downloaded from http://pubs.acs.org on August 15, 2015

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Molecular dynamics simulations of poly(ethylene oxide) grafted onto silica immersed in melt of homopolymers

Zuzana Benková,*,†,‡ M. Natália D. S. Cordeiro*,†

†

LAQV@REQUIMTE, Department of Chemistry and Biochemistry, Faculty of Sciences,

University of Porto, Rua do Campo Alegre 687, 4168-007 Porto, Portugal ‡

Polymer Institute, Slovak Academy of Sciences, Dúbravská cesta 9, 845 41 Bratislava,

Slovakia

*

To whom correspondence should be addressed:

e-mail: [email protected]; Fax: +351 220402659 e-mail: [email protected]; Fax: +351 220402659

1 Environment ACS Paragon Plus

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Abstract

Tuning of surface properties plays an important role in applications ranging from material engineering to bio-medicine/chemistry. The interactions of chains grafted to a solid support and exposed to a matrix of chemically identical chains represent an intriguing issue. In this work, the behavior of poly(ethylene oxide) (PEO) chains grafted irreversibly onto an amorphous silica and immersed in the matrix of free PEO chains of different polymerization degree is studied using molecular dynamics simulations. The density distributions of grafted and free PEO chains, height of the grafted layer, overlap parameters and order parameters depend not only on the grafting density but also on the length of free chains which confirm the entropic nature of the interactions between the grafted and free chains. In order to achieve a complete expulsion of the free chains from the grafted layer a grafting density as high as 3.5 nm–2 is necessary. Free PEO chains of 9 monomers leave the grafted layer at lower grafting densities than the longer PEO chains of 18 monomers in contrast with the theoretical predictions. The height of grafted layer evolves with the grafting density in the presence of free chains in qualitative agreement with the theoretical phase diagram.

Keywords: molecular dynamics simulations, poly(ethylene oxide) brushes, amorphous silica wetting, matrix of homopolymers


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1. Introduction Polymer coating of surfaces has found a large diversity of technological applications ranging from the stabilization of colloidal suspensions,1 the reversible tuning of wetting 2 and adhesion,3,4 to friction, lubrication and wear.5 Of special relevance is the polymer-coated surface immersed in a melt of chemically identical free polymers. Besides the technological utilization, such systems turn out to be identical with theoretically intriguing systems of two opposing surfaces grafted by polymers and exposed to a matrix of chemically identical polymers.6-8 At certain conditions, it is entropically more convenient to replace two brushmelt interfaces by a single brush-brush interface. The penetration of free chains from the matrix into a layer of end-grafted polymers is capable of repelling two opposing polymer-grafted surfaces. On the other hand, the expulsion of free chains from the layer of end-grafted chains triggers the attraction of two opposing polymer-grafted surfaces. These two entropically controlled phenomena are termed as the wetting and dewetting, respectively. In the case of repulsive surfaces, one can encounter the allophobic dewetting regime at low grafting densities and the autophobic dewetting regime at high grafting densities.8-12 The wetting regime is located between these two dewetting regimes. The transitions between these regimes depend on the grafting density σ and the number of monomers in the grafted and free chains N and P, respectively. The theoretical schematic diagrams (P, σ) for fixed N based on simple scaling arguments13-16 are shown in Figure 1. The regimes assigned by numbers in Figure 1b are as follows: 1) the mushroom regime of non-overlapping grafted chains with the excluded volume interactions between grafted and free chains, 2) the mushroom regime with ideal behavior of non-overlapping grafted chains, 3) non-stretched brush regime with ideal behavior of grafted chains, 4) the stretched brush regime with the excluded volume interactions, 5) the stretched brush regime with ideal behavior of overlapping grafted chains 6) the pseudo-ideal regime and 7) the


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dewetting regime with only marginal overlap of the free and grafted chains at the interface. The predicted transitions shown as lines in the logarithmic plot correspond to 1 ↔ 4 ~ / / ,

2 ↔ 3 ~ , 3 ↔ 5 ~ / ,

4 ↔ 5 ~ ,

5 ↔

6 ~ / and 6 ↔ 7 ~ / . The numerical prefactors of the order of unity are considered equal to 1, except for 5 ↔ 6 where the numerical prefactor was arbitrarily set to 0.63 in order to form a stripe assigning the pseudo-ideal regime in the state diagram. For a repulsive supporting surface, the transition between the allophobic dewetting and wetting regimes is approximately identified with the transitions to regimes 4 and 5, i.e. from the nonstretched to the stretched regimes. Regardless of the character of a supporting surface, the transition between the wetting and autophobic dewetting regimes conforms to the transition to regime 7 when the density of grafted chains attains the density of a melt of free chains. Notice, that the intersection of 3 ↔ 6 and 6 ↔ 7 transition lines is approximately for P ≈ N and σ ≈ N–1/2, meaning that the free chains which are longer than the grafted chains are supposed to leave the grafted layer and there is no wetting of a repulsive supporting surface anymore. Though, qualitatively the same diagrams but with different dependence of wetting12 and dewetting17 transitions based on the spreading parameter S were put forward as well. In the latter transition > 0 ↔ < 0 ~ / , the difference ensues from the different definition of the dewetting phenomenon when the transition to the dewetting regime is identified with the change of the sign of the spreading parameter from positive to negative values.16 The ensuing transition scaling is also included in Figure 1 (dashed line). In contrast to P–1/2 dewetting scaling13-16 and NP–3/2 dewetting scaling17, the self-consistent field theory proposes N3/2P–2 dependence.7 For an attractive surface, only the wetting-autophobic dewettig transition is anticipated.


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a)

N

b)

2/3

h = aNσ '

6.868

1

6

-1/4

σ ' 1/2

5

N h = aNP

-1/3

σ'

1/3

h = aN h = aNP N

-1/3

4

1

3 0.5

1/2

1/3

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h = aN P

-6/5

-1/2

-2

NP

7

7

σ/nm

h=a

S0

h = aNσ '

σ'

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N h = aN

-1/5

1

N

0.1

1/2

N

1/2

2

1

-1

1

4.243

10

P

P

Figure 1. Schematic , diagram ( , with a being the size of a monomer) in the logarithmic scale for grafted polymers of fixed N monomers exposed to a matrix of free homopolymers of P monomers. The height h of grafted polymer layer in the outlined regimes is also included in (a). The same as in (a) adopted for PEO chains with N = 18 and P shown in the abscissa (b). The delimited areas correspond to the different regimes specified in the text. The dashed line delineates the region of partial and complete dewetting characterized by positive and negative spreading parameter S, respectively. The symbols in (b) stand for the combination of parameters used in the present atomistic molecular dynamics simulations.

The pioneering study of the interface between a layer of grafted polymers and chemically identical chains based on scaling arguments dates back to 1980.13 Since then a great deal of related theoretical works has appeared. These in turn have been mostly focused on the analytically solvable limits of densely grafted chains with σ >> N1/2 and of either P > N

15,16,18-20

though this is far from experimental and application

conditions.19,21 To study systems where P ≈ N theoretically, one is left with a numerical selfconsistent-field (SCF) approach.7-9,17,22-24 However, the numerical approaches have been


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mostly elaborated for either very low or very high coverage densities, again far from real systems. The comparison of the theoretical predictions with the experimental results, on the other hand, is restricted only to a few combinations of N, P and σ parameters because of the difficulty to prepare grafted polymer layers of high enough and often even of well-defined grafting densities. The additional limitations lie in rather short contour lengths of the grafted chains. While an ample number of theoretical works renders the phase diagrams (P, σ) or alternatively (P/N, σ) for polymer-coated surfaces immersed in a homopolymer matrix,7,13-16 related experimental works are scarce and are rather restricted to small interval of variable parameters, e.g., the phase diagram for polystyrene grafted surface in the presence of a melt of polystyrene12 or for polystyrene grafted nanoparticles dissolved in a matrix of free polystyrene.25 However, since in the latter experimental measurements the chains have been grafted on curved surfaces, the comparison of the phase diagram with the theoretically constructed phase diagrams is limited to the qualitative rather than quantitative level. Moreover, the theory assumes completely flexible chains, sharp boundaries at interfaces and homogenous distribution in the plane parallel to the supporting substrate. Experimental investigations10,12,21,26,27 lead to some findings, e.g., insensitivity of the free-chain penetration to the grafting density, the influence of finite compressibility of the polymer melt on the autophobic behavior or the significant increase of contact angle of melt with the brush thickness, which are still not fully addressed quantitatively by theoretical treatments. The observed discrepancies originate from phenomena that may not be incorporated at the theoretical level. This is indeed a field for employing atomistic molecular simulations as a bridge between the theory and experiment. These simulations might explain the above mentioned inconsistencies. Till now, however, almost all simulations have been based on coarse-grained approaches.11,28-32 Nevertheless, as the experimental results reveal, this approximation is not always an adequate description and one has to take more subtle


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atomistic details into account. Since coarse-graining neglects the specific interactions between atoms one of its shortcomings, relevant to surface-grafted polymers interacting with melt of free polymer chains, is the shift in entropy due to the reduced number of degrees of freedom. Only a small number of atomistic molecular simulations of grafted chains immersed in the matrix of homopolymers have been reported33-35 and none of these studies dealt with systematic variation of P/N and σ parameters to investigate the state diagram of surfacegrafted polymers in the presence of free chemically identical polymers. The aim of presented study is to explore the wetting behavior of a system composed of a solid surface being an amorphous silica which supports a layer of the end-grafted poly(ethylene oxide) (PEO) chains and is placed in a chemically identical polymer melt using fully atomistic molecular dynamics simulations. PEO is chosen because of its tremendous technological36 and biological applications37 and its peculiar unique characteristics such as an amphiphilic nature, perfect solubility in water and organic solvents, biocompatibility, low immunogenicity and non-toxicity.38,39 The length of tethered chains (N monomers) is kept constant while the length of the free chains (P monomers) is varied in order to study different regimes delineated in the theoretical (P, σ) diagram, i.e., P < N1/2, N1/2 < P < N, P = N. In order to simulate the real experimental proportions, both lengths P and N are of the same order. The grafting densities of the substrates span the range from the mushroom (nonoverlapped regime) to the strongly-stretched brush (overlapped) regime with highly orientated PEO polymer chains in a liquid-like ordered state.40 By analysis of the monomer density distributions, overlap parameter, height and orientation order parameter of the grafted PEO layer in the absence or presence of free PEO chains, the simulations are supposed to shed light into the behavior of PEO chains tethered to the amorphous silica surface and immersed in the melt of free PEO chains partially or completely penetrating the grafted layer.


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2. Methodology

In the presented study, fully atomistic molecular dynamics (MD) simulations were employed in order to scrutinize a system composed of the flat surface of amorphous silica covered with the layer of monodisperse PEO chains comprising N = 18 monomers. These chains are irreversibly attached to the silica surface, which exhibits an attractive affinity for ethylene oxide (EO) monomers, by chemical bonds through the oxygen atoms. The free ends of the grafted PEO chains were terminated by methyl groups. The contour lengths of free PEO chains were P = 3, 9, and 18 monomers. The parameter combinations (P, σ) used in the presented simulations are shown as symbols in Figure 1b. The substrate was 0.8 nm thick. Such a thickness was sufficient for the attractive interactions not to be underestimated. In contrast to the theoretical assumptions, such a point-like modeling of substrate accounts for a finite roughness as is the common case in experimental conditions. As an example, a snapshot of the simulated system composed of PEO chains grafted at σ = 0.218 nm–2 and exposed to the matrix of free chains of P = 3 is shown in Figure 2. The atoms of the silica substrate were kept frozen during the MD simulations and participated only in non-bonded interactions with the atoms of PEO chains. The non-bonded interaction parameters for silicon and oxygen atoms building the silica substrate are listed in Table S1 (SI). The surface layer was aligned with the xy plane in the Cartesian coordinate system. The grafting density σ of grafted PEO chains, expressed as the number of chains attached to a unit area, spanned the interval 0.055 - 3.495 nm–2. All MD simulations were performed using the GROMACS package.41,42 The all-atom intra- and intermolecular interactions were described by the revised CHARMM force field.43,44 The interactions between different atom species were determined using the Lorentz-Berthelot combining rule, i.e.: σij = (σi + σj)/2 and εij = (εijεij)1/2. Besides the PEO-grafted surface immersed in the matrix


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of free PEO chains also the PEO-grafted surface in the absence of free PEO chains were simulated (dry conditions) for comparative purposes. Further details on MD simulation procedure are described in Supporting Information (SI).

3. Results and discussion

3.1. Density distributions

Figure 2 illustrates the changes in the conformation of PEO chains grafted at σ = 0.218 nm–2 which are induced by wetting with short PEO chains (P = 3). Throughout this work, PEOg and PEOf stand for the grafted and free PEO chains, respectively. As one can notice, the initial pancake-like conformation of PEOg chains ensuing from the separate simulations in the absence of PEOf chains considerably expands away from the attractive silica substrate when exposed to the melt of PEOf chains. At this grafting density, the short free chains readily penetrate the grafted layer and supply the function of a good solvent. Thus in spite of the attractive interactions between the amorphous silica and end-grafted PEO chains, the interactions between the PEOg and much shorter PEOf chains dominate the final conformation (Figures 2b, 2c). As a consequence, the grafted chains are stretched away from the silica substrate instead of adopting pancake conformation typical for this combination of N and σ values at dry conditions.40


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b)

a)

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c)

Figure 2. Snapshots of the initial conformation after the combination of the two separately equilibrated blocks (a) and final conformations after 50 ns of MD simulations at T = 298 K (b) of PEO chains (N = 18) grafted at σ = 0.218 nm–2 in the presence of the matrix of free PEO chains (P = 3). Snapshot (c) corresponds to snapshot (b) after omitting the free PEO chains.

The density distribution functions of PEOg and PEOf chains in the composed systems along the normal of the silica substrate for different grafting densities, which have been evaluated from the last 20 ns of simulations, render valuable qualitative insight into the degree of overlap and mutual intermixing between the layer of PEOg chains and the matrix of PEOf chains. In addition to these density distributions, Figure 3 also provides the density distributions of corresponding dry PEOg chains and the density distributions of PEOf chains above the bare silica substrate. At the same time, the density distributions are valuable for more quantitative analysis arising from the overlap parameters and height of the grafted layer discussed later.


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a)

b) σ = 0.218 nm-2

N = 18 grafted PEO in matrix dry grafted PEO P=3 matrix over coated SiO2

1.2

matrix over bare SiO2

0.6

0.0

1.2


0.6

0

1

2

3

4

0.0

5

z/nm

c)

0

1

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σ = 3.495 nm-2

ρ/g.cm-3


0.8

0.4

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P=9 matrix over coated SiO2

0.4

0.0 0

1

2

3

e)

4

5


ρ/g.cm-3

0.8

0.0

P = 18 matrix over coated SiO2

1

2

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4

3

4

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5

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8

9

z/nm N = 18 grafted PEO in matrix dry grafted PEO

1.2

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P = 18 matrix over coated SiO2 matrix over bare SiO2

0.4


0

2

1.6

1.2

0.4

1

σ = 3.495 nm-2

N = 18 grafted PEO in matrix dry grafted PEO

1.6

0

f)

z/nm σ = 0.218 nm-2

8

1.2


0.0

7

N = 18 grafted PEO in matrix dry grafted PEO

1.6

1.2

5

z/nm

d)

σ = 0.218 nm-2

1.6

ρ/g.cm-3


σ = 3.495 nm-2

1.8

ρ/g.cm-3

ρ/g.cm-3

1.8

ρ/g.cm-3

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0.0

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z/nm


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2

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z/nm

6

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Figure 3. Density distribution of PEOg and PEOf chains in the composed systems as a function of the distance from the silica surface for different grafting densities and PEOf chain lengths. Density distributions of dry grafted PEO chains and free PEO chains above the bare silica substrate are also included for comparison.

The comparison of the density distributions for PEOg chains in the presence and in the absence of the matrix of PEOf chains of P = 3, 9 and 18 monomers in Figures 3a, 3c, and 3e, respectively, reveals that at low grafting densities, PEOg chains tend to expand away from the attractive silica substrate and mix with PEOf chains. The matrix of PEOf chains with P = 3 monomers is supposed to function as a good solvent in the regime of non-overlapped PEOg chains with N = 18 monomers (P < N1/2). On the other hand, in this regime, the matrix of longer PEOf chains with P = 9 and 18 monomers is expected to exhibit features salient for a theta (Θ) solvent (P > N

1/2

) (see SI for the explanation). It appears from the larger extension

of PEOg chains in the presence of short PEOf chains that these predictions work also for chains grafted at small densities in the presence of free homopolymers according to the phase diagram (Figure 1). In both cases, the melt of PEOf chains is responsible for the swelling of the layer of PEOg chains, regardless of the length of PEOf chains. Thus from Figures 3a, 3c, and 3e it follows that, two opposing silica surfaces which are in the mutual mirror image relation should exhibit repulsive interactions when being grafted with PEO chains of N = 18 at commonly accessible experimental grafting density ~ 0.2 nm–2

45-48

and immersed in the

matrix of free PEO chains of P ≤ 18. However, the simulations of systems composed of two mirror-image related surfaces are necessary for unambiguous assertion. The common feature for the all density distribution functions in Figures 3a, 3c and 3e is the rich structuring of free as well as grafted PEO chains in the vicinity of the attractive silica surface. In a system composed of both PEOg and PEOf chains, the peak amplitudes of


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the layered structure are diminished, however, the positions of these amplitudes remain unaltered when compared with the separate systems of a dry PEOg layer or a melt of PEOf chains interacting with the bare silica surface. This is not surprising since in a system composed of both PEOf and PEOg chains both chain types experience competitive attractive interactions with the silica surface. The exception is the system composed of PEOf chains of 9 monomers in which the intensity of the first peak due to PEOg chains remains virtually the same as in the system of dry PEOg chains. This indicates a hampered mixing between PEOg and PEOf chains of this length and will be also observed in other investigated properties of the present systems. As one can see from the density distributions presented in Figures 3b, 3d and 3f, the PEOf chains are not susceptible to penetrate through the grafted layer at σ = 3.495 nm–2, though there is small residual overlap at the interface of PEOf and PEOg chains. The nonvanishing penetration length in the dewetting regime has also been reported by Gay using a theoretical approach.16 The suppressed structured layering in the density of PEOg near the silica substrate is associated with reduced density fluctuations in more condensed systems. The average densities of PEOf chains in the melt above the grafted layer are 0.939 g.cm–3, 1.065 g.cm–3 and 1.097 g.cm–3 for P = 3, 9 and 18 monomers, respectively. These data agree fairly well with experimental values of 0.937 g.cm–3,49 1.05 g.cm–3,50 and 1.08 g.cm–3,51 respectively. As the intensity of the first and second peak in the density distributions of short PEOf trimers (P = 3) demonstrates these chains are organized in a denser manner near more densely grafted silica when compared with longer PEOf nonamers (P = 9) and octadecamers (P = 18) (Figure S1 in SI for the density distributions of PEOf chains above the silica substrate grafted by PEOg chains at different grafting densities). The intensity of these peaks is independent of the length of PEOf chains at sufficiently small grafting densities similarly to the case above


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the bare silica substrate. However, there is already a reduction in the density of PEOf trimers in the second layer and higher layers which reflects the lower density of PEOf trimers in a bulk phase. The bulk density of PEOf chains is recovered already at the distance of 2 nm from the bare and sparsely covered silica surface while the densely grafted PEOg chains cause depletion in the density of PEOf, especially for PEOf trimers. It should be noted here that at lower grafting densities, PEOf chains have diffused through the grafted layer towards the silica substrate already at the very beginning of the simulation phase at 400 K for all PEOf chain lengths. The time evolution of the density profiles does not indicate any desorption process of PEOf. The behavior of PEOf nonamers breaks the expecting trend (Figure 1). At σ = 0.218 nm–2, the density of PEOf nonamers in the first layer considerably drops below the bulk density and also below the density of longer PEOf octadecamers which indicates that PEOf nonamers leave the grafted layer more readily than the longer PEOf chains. In the case of PEOf octadecamers, the reduction in the first layer is observed at σ = 0.437 nm–2 whereas PEOf trimers remain still deeply inserted in the grafted layer even at σ = 1.092 nm–2, i.e., at the grafting density which approaches the present-day experimental upper limit.52-54 However, at this grafting density, the first peak already drops below the bulk density. As the intensity of the first peak indicates, the PEOf trimers are getting detached from the silica surface at σ ~ 1.3 nm–2. The mixing of PEOf trimers with the peripheral layer of PEOg is still observed at a grafting density as high as 2.622 nm–2 as demonstrated by the left shoulder in the density distribution function of PEOf trimers. It is worth mentioning that at this and higher grafting densities the dry layer of grafted PEO chains exhibits properties typical of a nematic liquidlike phase.40 At σ = 3.495 nm–2, the depletion zone in the density distribution in the vicinity of the silica substrate spreads behind the height of the grafted layer even for PEOf trimers and does not depend on the number of monomers constituting the PEOf chains. This evidences the


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complete dewetting of the grafted PEO layer. Since so far such a high grafting density is experimentally not accessible it follows that one can hardly achieve the adhesion of two opposing silica surfaces irreversibly coated with not too long PEO chains in the presence of free PEO chains of shorter or comparable molar weight. In other words, it turns out to be practically impossible to dewet the silica substrate covered with short PEO chains. The depletion zone between the PEOf chains and the silica substrate which may also be assumed as a criterion for dewetting initiation is observed at σ = 2.185 nm–2 for trimers, at σ = 1.092 nm–2 for nonamers and at σ = 1.311 nm–2 for octadecamers. Notice, that the onset of the brush regime for PEOg chains of N = 18 monomers in dry conditions was recognized at σ ~ 1.7 nm–2.40 Again, in agreement with the above findings, the shorter nonamers tend to escape from the grafted layer more readily at lower grafting densities than the longer octadecamers. The underlying difference in the density distributions between the dry grafted layer and the grafted layer exposed to the melt of free PEO chains is the steep step-like decay in the density distribution at the edge of dry layer which becomes attenuated upon inter-digitation with the melt of free PEO chains at denser coverages. (Figure S2 in SI). Interesting is the formation of the second peak in the density distributions of PEOg chains which is observed already at grafting density of 0.218 nm–2 in the presence of PEOf trimers while this peak is formed at 0.874 nm–2 in the presence of PEOf nonamers and, in contrast to the former case, is always of lower intensity than the first peak. Due to the absence of this second peak in the density distribution of PEOg chains at 0.218 nm–2 in the presence of PEOf nonamers the edge of grafted layer is spread further from the silica surface than in the presence of PEOf trimers. Figure 4 displays the lateral density distribution functions which are normalized to unity and disprove the formation of laterally inhomogeneous aggregates even at lower grafting densities (Figure 4a). The insertion of PEOf chains into the grafted layer does not


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bring about qualitative changes in the lateral distributions of the grafted layer. The only difference lies in the magnitudes of the density amplitudes being enhanced in the presence of PEOf nonamers and octadecamers. The longer PEOf chains tend to fill the available space in the grafted layer and thus develop a lateral pressure on the PEOg chains which in turn leads to a local densification within the grafted layer. The short PEOf trimers affect the lateral density less significantly. Interestingly, a little local densification and rarefaction in the lateral structure is also preserved at a grafting density as high as 3.495 nm–2 when the PEOf chains penetrate only the peripheral grafted layer (Figure 4 b).

a)

b) P = 3 σ = 0.218 nm-2 P=9 P = 18 dry

0.5 0.4

P=3 P=9 P = 18 dry

0.28

σ = 3.495 nm-2

σ

0.26 σ

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0.3

0.24 0.2

0.22 0.1 0.0

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(x = y)/nm

1

2

3

(x = y)/nm

Figure 4. Lateral density distribution normalized to unity for PEOg chains grafted at σ = 0.218 nm–2 (a) and σ = 3.495 nm–2 (b) exposed to the matrix of PEOf chains of P monomers. Lateral density distribution for dry PEOg chains is also included for comparison.

3.2. Overlap parameter


4

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The overlap between the grafted PEO layer and the matrix of free PEO chains might be quantified by the overlap parameter defined from the density distributions as follows:

!

, "- #$%&' ()#$%&* (+( , , "- #$%&'(+()"- #$%&* (+(

(1)

The alternative way of quantifying the overlap between the grafted layer and free melt of PEO chains is to introduce some dimensionless parameter Aov, for instance, to evaluate the common area of respective density distributions and normalize it by the integrated density distribution of PEOg chains. Thus, the total overlap is associated with Aov = 1

a)

b) 1.00

0.25

P=3 P=9 P = 18

0.20

P=3 P=9 P = 18

0.75

0.15

Aov

Pov/nm-1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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0.50

0.10

0.25

0.05 0.00 0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

0.00 0.0

0.5

1.0

1.5

2.0

2.5

-2

σ/nm

-2

σ/nm

Figure 5. Overlap parameter between PEOf chains of P monomers and PEOg chains of N monomers grafted on the silica substrate as a function of the grafting density defined in equation 1 (a) and as a common area of PEOf and PEOg density distributions normalized by the integrated PEOg density distribution (b).


3.0

3.5

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In Figures 5a and 5b, both overlap parameters display the same trend and render more quantitative insight into the overlap between the layer of PEOg and the melt of PEOf chains. For all PEOf contour lengths, the overlap parameter globally decreases with the increasing grafting density except for a little local increasing tendency around σ ~ 1.5 nm–2, when the PEOf chains are losing direct contact with the silica substrate. Both overlap parameters are larger for trimers. In contrast with the theoretical predictions and in agreement with the observations in the density distributions discussed above, the system composed of PEOf nonamers exhibits smaller overlap parameter than the system composed of PEOf octadecamers in the range of lower grafting densities in which the dry layer of PEOg chains adopts predominantly pancake-like conformation.40 On the other hand, the overlap of PEOf nonamers becomes larger than the overlap of PEOf octadecamers at grafting densities at which the dry grafted layer adopts brush conformation. At σ ~ 2.2 nm–2, which is approximately the grafting density at which the dry PEOg chains start to be ordered in a nematic manner,40 the overlap parameters for PEOf nonamers and octadecamers are indistinguishable. The overlap parameter for PEOf trimers attains the same value as the overlap parameters of longer PEOf chains at σ = 3.495 nm–2. Thus at this grafting density, the PEOg chains are organized so densely that there is no space for free PEOf chains to be inserted, regardless of their different molar mass.

3.3. Height of the grafted layer

The influence of PEOf insertion into the layer of PEOg chains is well recognizable on the evolution of the height of the grafted layer with the grafting density in the presence of PEOf chains shown in Figure 6. The height of the grafted layer was evaluated as the normalized first moment of the PEOg density distribution, i.e. as:


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,

ℎ

"- ()#$%&' (+( , "- #$%&'(+(

(2)

The grafting density at which the complete dewetting occurs might be well identified with the value at which the plots of h vs. σ for the grafted layer in the presence of the PEOf matrix collapse with the plot for dry layer also shown in Figure 6. The solid line in Figure 6a indicates slope 1 which represents the characteristic scaling of the height of dry brush layer with the grafting density, i.e.,

ℎ ≈ ′

(3)

where a is the monomer size and is the dimensionless grafting density. As was mentioned above, depending on the length of PEOf chains the matrix of PEOf chains behaves like a good or Θ solvent with respect to non-overlapped grafted PEOg chains. At higher grafting densities, the height dependence of grafted layer in a good and Θ solvent is supposed to scale with the grafting density, respectively, as:

ℎ ≈ / ′/

(4)

ℎ ≈ /1 ′/

(5)

Thus before free chains leave the grated layer, the grafted layer is supposed to pass from the good solvent conditions (equation 5) to the Θ solvent conditions (pseudo-ideal regime). Remarkable is the same scaling P–1/2, though with different numerical prefactors, for the transition dependences 5 ↔ 6 and 6 ↔ 7 (Figure 1a). 19 Environment ACS Paragon Plus

Langmuir

a)

b)

2.0

2

N = 18

N = 18

1.6

1 1.2

P=3 P=9 P = 18

0.8

P=3 P=9 P = 18

0.5

dry brush slope = 1

0.4 0.0

h/nm

h/nm

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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0.5

1.0

1.5

σ/nm

2.0

2.5

3.0

slope = 1/3 slope = 1/2 3.5

0.1

0.5

σ/nm

-2

1

-2

Figure 6. Height of PEOg chains of N monomers grafted on the silica surface in the presence of PEOf chains of P monomers as a function of the grafting density. The evolution of the height of PEOg chains at dry conditions is also included. The solid black line serves as a guide to the eye and represents theoretically predicted scaling of the height for a dry brush layer (a); the same as in (a) in logarithmic scale (b). The solid and dashed line, respectively, represent the characteristic scaling predicted for the good-solvent and pseudo-ideal conditions.

The variation of the height of the grafted layer with its grafting density in the presence of free homopolymers might be compared with analytically predicted dependences outlined in Figure 1b. Since the relations constituting the borderlines between the regions in Figure 1 tacitly presume that the numerical constants are set to unity or in the case of 6 ↔ 7 to an arbitrary value different from unity, the borderlines should be taken qualitatively rather than quantitatively. Anyway, in the presence of PEOf chains, the evolution of the height is supposed to be independent of the grafting density for smaller grafting densities in the nonoverlapped regime and should scale with σ1/3 for more densely grafted PEOg chains. The interval of σ1/3 scaling is narrowing as the length of PEOf increases. Between this good-


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solvent regime and the dewetting regime the pseudo-ideal regime is anticipated with characteristic σ1/2 scaling of the height. What one observes in Figure 6b is an initial steady behavior of the plots for PEOf trimers and nonamers which is followed by a gradual increase with the slope close to 1/3 and 1/2 till it reaches the steeper increase of slope 1 in the dewetting regime. The h vs. σ dependence for PEOf octadecamers initially increases. The absence of the steady initial trend in the height evolution with the small grafting densities is most likely a consequence of entanglement formations between the sparsely grafted chains from the silica surface and PEOf octadecamers. However, there is an interval of grafting densities where the h vs. σ plot exhibits a plateau which is followed by an abrupt increase with the slope close to unity. This behavior is in consistency with Figure 1b where one can notice that the stretched brush regime with the excluded volume interactions between grafted chains disappears when P ≈ N. On the other side, the existence of the stretched brush regime with the excluded volume interactions or pseudo-ideal statistics between PEOg chains in the presence of bulk PEOf trimes is proven by less abrupt increase of h vs. σ before dewetting occurs (see the slopes in Figure 6b). At σ ≈ 3.495 nm–2 all curves collapse with the curve of the dry PEOg layer. The h vs. σ plots of PEOg layer in the presence of PEOf nonamers and octadecamers converge on the h vs. σ plot of dry PEOg layer more readily than in the presence of PEOf trimers. At grafting densities corresponding to the non-overlapped regime of dry PEOg layers,40 the grafted layer is most significantly expanded away from the silica surface when the matrix of PEOf chains contains trimers and least when it contains nonamers. This trend mirrors the susceptibility of PEOf octadecamers to penetrate the grafted layer more than PEOf nonamers do. This finding along with the trends in the above mentioned properties suggests that the longer octadecamers are more efficiently incorporated into the grafted layer than the shorter nonamers at lower grafting densities. When the grafting density exceeds ~ 1.2 nm–2, the PEOg layer becomes


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slightly higher in the presence of the PEOf nonamers than in the presence of the PEOf octadecamers, as expected from Figure 1 and Figure 5.

3.4. Orientation order parameter

The space restrictions imposed by the silica surface influences also the bond orientation of PEOg chains. The orientation preference of the effective bonds with respect to the surface normal might be well deduced from the first- and second-rank orientation order parameters defined as the first and second Legendre polynomials and , respectively.

〈 cos 6〉 〈cos 6〉

(6)

〈 cos 6〉 3〈cos 6〉 − 1

(7)

Here, the effective bond is defined as a line connecting two consecutive oxygen atoms along the chain backbone and θ denotes the angle between this bond and the surface normal. The behavior of the orientation order parameters is dictated by the grafting density and interactions of PEOg chains with the silica surface as well as with PEOf chains. The increasing grafting density should enhance the orientation order parameters of PEOg chains while the attractive interactions of PEOg chains with the silica surface are supposed to reduce and . However, the formation of nematicaly collapsed conformation might even enhance values. The insertion of PEOf chains into the grafted layer is expected to diminish the interactions of PEOg chains with the silica surface and the final


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effect on the and depends on the length of PEOf chains (entanglements and excluded volume effects). Figures 7a and 7b displaying and parameters of very sparsely grafted chains (σ = 0.055 nm–2) suggest that the insertion of PEOf trimers into the grafted layer affects its conformation more significantly than the insertion of PEOf nonamers and octadecamers. The positive values of both parameters caused by the presence of PEOf trimers mean stretched PEOg chains. The oscillating behavior of parameter around zero value and of around negative value characteristic for the dry grafted layer points to adsorbed disorder conformation of dry PEOg chains. These trends are preserved also after the insertion of PEOf nonamers and octadecamers, however, upon the insertion, the amplitudes are getting elongated and, in the case of the parameter, are also shifted towards more positive values, especially for PEOf octadecamers. This is most likely a consequence of the stronger interdigitation of PEOg chains with PEOf octadecamers than with PEOf nonamers. The absence of amplitudes in the and parameters for systems containing PEOf trimers originates from the disability of short PEOf trimers to form entanglements with PEOg chains. As the grafting density of PEOg chains in the presence of PEOf trimers increases, the orientation of the PEOg chain segments with the surface normal is diminished till σ = 0.218 nm–2 (Figures 7c and 7d) as one can see in the reduced values of and parameters when compared with Figures 7a and 7b. Such a reduction might be explained by the declined density of PEOf trimers in the first structured layer (Figure S1d in SI). Thus the PEOg chains achieve space to be adsorbed onto the silica substrate and to become also more disordered alone their backbones. Worth noting are also the significant amplitudes in and parameters observed in the presence of PEOf octadecamers which indicates a formation of locked loop-like conformation of PEOg chains at


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this grafting density. On the other hand, PEOf nonamers only negligibly affect the order parameters of PEOg chains when compared with dry PEOg chains. However, the presence of free chains, regardless of their length, amplifies the alignment of grafted chains with the surface normal. Continuos transition The further increase of the grafting density leads to the enhancement of both and parameters (Figures 7e and 7f) and to the suppression of the amplitudes. The larger values of both order parameters for PEOg chains exposed to PEOf chains than for dry PEOg chains point out more significant stretching caused by the inserted PEOf chains. Finally, at σ = 3.495 nm–2 (Figures 7g and 7h), the order parameters for PEOg chains interacting with the matrix of PEOf chains attain the behavior characteristic for dry densely grafted PEO chains, i.e., initial damped oscillations around a plateau followed by a steep decline indicating strongly stretched chain conformation with more flexible free ends of PEOg chains.


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a)

b) σ = 0.055 nm-2

0.6

0.6

P=3 9 18 dry

0.9

0.3 0.0

-0.6

σ = 0.055 nm-2

0.3

0.0

0.2

0.4

0.6

0.8

-0.6

1.0

0.2

0.4

i/N

0.6

0.8

1.0

i/N

c)

d) P=3 9 18 dry

0.6

P = 3 σ = 0.218 nm-2 9 18 dry

0.2

σ = 0.218 nm-2

P=3 9 18 dry

-0.3

-0.3

0.4 0.2

0.0

-0.2

0.0 -0.2

-0.4 0.2

0.4

0.6

0.8

1.0

0.2

0.4

i/N

e) P=3 9 18 dry B

0.2

0.2 σ = 1.092 nm-2

0.4

0.8

1.0

σ = 1.092 nm-2 P=3 9 18 dry

0.1

0.0

-0.1

0.0

-0.2

0.6 i/N

f)

0.6

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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0.2

0.4

0.6

0.8

1.0

-0.2

0.2

0.4

0.6 i/N

i/N


0.8

1.0

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g)

h)

0.60 σ = 1.748 nm-2

0.30 P=3 9 18 dry

0.15

σ = 1.748 nm-2

0.2

0.45

P=3 9 18 dry

0.1

0.0

0.00

-0.1 0.2

0.4

0.6

0.8

1.0

0.2

0.4

i/N

i)

0.6 i/N

0.8

j) σ = 3.495 nm-2

0.60

P=3 9 18 dry

0.45

σ = 3.495 nm-2

0.5

0.75

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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0.4 0.3 P=3 9 18 dry

0.2

0.30

0.1 0.2

0.4

0.6 i/N

0.8

1.0

0.2

0.4

0.6

0.8

i/N

Figure 7. Dependence of the orientation order parameters with respect to the surface normal (a, c, e, g, i) and (b, d, f, h, j) of consecutive effective bonds of PEOg chains on the contour distance from the silica substrate for different grafting densities and lengths of PEOf chains.


1.0

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4. Conclusions

The present atomistic molecular-dynamics simulations are focused on the structural properties of PEO chains (N = 18 monomers) end-grafted onto the amorphous silica surface and immersed in a matrix of chemically identical chains. In order to compare the behavior of a realistic system with the state diagram, followed from the theoretical model, large interval of grafting densities of PEOg chains (σ = 0.055-3.495 nm–2) and three representative lengths of PEOf chains (N = 3, 9 and 18 monomers) were considered in the simulations. The presence of PEOf chains induces expansion of the PEOg chains from the silica surface which acts as an attractive support for PEO chains. Furthermore, the matrix of PEOf chains behaves like a solvent in line with the theory for good and Θ solvent and the sparsely grafted PEOg chains expand more when exposed to the matrix of shorter PEOf trimers than to the matrix of longer PEOf nonamers and octadecamers. Moreover, as the structural pattern of the density distribution functions suggests, PEOg and PEOf chains display competitive interactions with the attractive silica surface at lower grafting densities. Surprisingly, the PEOf nonamers tend to lose their direct contact with the silica support already at lower grafting densities than the PEOf octadecamers. This tendency might be attributed to the enhanced entanglements formed between the longer PEOf octadecamers with PEOg chains and locked loop-like arrangement of PEOf octadecamers evidenced by the orientation order parameters. As anticipated, PEOf trimers remain in the vicinity of the silica surface also at higher grafting densities. At lower grafting densities the overlap of the PEOf nonamers with the grafted layer is smaller than the overlap of PEOf octadecamers, however, the overlap of PEOf nonamers becomes larger after the PEOf chains become detached from the silica support. While the overlap parameters of PEOf nonamers and octadecamers start to be virtually the same from


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the grafting densities of ~ 2.2 nm–2, the PEOf trimers are still more significantly mixed with the grafted layer at this coverage. Although, at σ = 3.495 nm–2, the overlap parameters still indicate little overlap between PEOf and PEOg chains, these parameters merge into one value for all PEOf chain lengths. The variation of the height of the grafted layer with the grafting density for the real systems qualitatively agrees with the theoretical predictions for model polymers. The orientation of PEOg chains with the surface normal depends on the length of PEOf chains more substantially at lower and moderate grafting densities, while as the PEOf chains are getting expelled from the grafted layer at larger grafting densities the differences are diminished. It is shown that very large grafting densities are necessary for the layer of relatively short PEO chains grafted onto the amorphous silica substrate to become dewetted from shorter or equally long free PEO chains. In practice, such grafting densities (3.5 nm−2) are not achievable. It turns out to be difficult even to achieve the detachment of PEOf chains from the silica substrate. Thus, two opposing surfaces covered with irreversibly grafted short PEO chains should not adhere in the presence of bulk free PEO chains of shorter or comparable molar masses. The results of this paper are also supposed to be useful in the “grafting to” synthesis when polymer chains are grafted to a functionalized surface. The further stage of this study is to address the effect of the surface curvature and thus to investigate the systems of a nanoparticle grafted by short PEO chains immersed in the melt of comparably long homopolymer chains.

Supporting Information


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Further details of the atomistic molecular dynamics simulations and of the theoretical concept of classifying the solvent quality as well as the derivation of the height dependence of a grafted layer in the strongly stretched regimes using the Flory approach. Two figures showing additionally the density distribution of free (Figure S1) and grafted (Figure S2) PEO chains along the surface normal for different grafting densities and lengths of the free PEO chains. This material is available free of charge via Internet at http://pubs.acs.org.

Acknowledgements This work was supported by a postdoctoral grant SFRH-BPD-90265-2012 (Z.B.) co-financed by the European Social Fund. Thanks are also to FEDER for financial support to LAQV@REQUIMTE, Project UID/QUI/50006/2013, as well as to Grants SRDA-0451-11 and VEGA 2/0093/12. The work also received financial support from the European Union (FEDER funds) under the framework of QREN through Project NORTE-07-0124-FEDER000067-NANOCHEMISTRY.

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Table of Contents Graphic

Molecular dynamics simulations of poly(ethylene oxide) grafted onto silica immersed in melt of homopolymers

Zuzana Benková, M. Natália D. S. Cordeiro

50 ns


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Molecular Dynamics Simulations of Poly(ethylene oxide) Grafted onto

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