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Kinetics of the Generation of Surface-Attached Polymer Networks through C, H‑Insertion Reactions M. Körner, O. Prucker, and J. Rühe* Department of Microsystems Engineering (IMTEK), University of Freiburg, 79110 Freiburg, Germany ABSTRACT: We describe the formation process of thin films consisting of surface-attached polymer networks formed through C, H-insertion based cross-linking (CHic process). To this thin films of polymers containing benzophenone or sulfonyl azide groups are photochemically or thermally activated, which leads to simultaneous cross-linking and surface attachment of the deposited polymer. A simple percolation model is used to describe the formation of such polymer networks as a function of reaction time and reaction conditions. It is based on known parameters such as the kinetics of the activation of the cross-linker, cross-linker contents, molecular weight of the polymer, film thickness, temperature (respectively the light dose), and absorption coefficient of the polymer. The developed model allows, with only one adaptable parameter, namely the efficiency factor j, the prediction of the complete cross-linking behavior of CHic reactions. The kinetic model enables the identification of suitable conditions for network formation and thus facilitates to use this very simple and versatile method to generate tailor-made surfaces.

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INTRODUCTION Many different strategies for the chemical modification of solid surfaces through covalently attached polymers have been developed in recent years. This includes the formation of self-assembled monolayers (SAM),1−3 grafting through processes, where a SAM of a monomer is used to form a surfaceattached polymer layer,4 the chemisorption of polymers (“grafting to”),5,6 or the growth of polymers through surfaceinitiated polymerization (“grafting from”).5−8 An interesting alternative to the formation of such monomolecular layers is the formation of surface-attached polymer networks from reactive precursor polymers because it allows the generation of comparably thick and very robust layers. When reactive precursor polymers are used, first the film can be formed by standard deposition protocols such as spin or dip coating, and then it is cross-linked and attached to the surface while the film is in the solid state. Cross-linking of such polymers in the glassy state can be performed by Diels−Alder reactions9−11 or by 2 + 2 cycloadditions,12 by Huisgen cycloaddition (“click chemistry”),13−16 and by addition of low molecular weight cross-linkers, such as in vulcanization reactions. In the latter case, however, phase separation of the two-component system might lead to heterogeneous films, so that in many cases a one-component system seems desirable. A major disadvantage of such cross-linking reactions is that in all of them the linking reaction takes place between two reaction partners, which have to find each other to create a link between the chains. This might be rather difficult in a solid, glassy film, especially if the concentration of the cross-linker in the film is rather low. As a result, the cross-linking reaction becomes rather slow with increasing conversion and many still unreacted groups remain in the film. © XXXX American Chemical Society

An interesting alternative to the described methods is to use reactions in which only one reactive group is contained, which after activation reacts with the neighboring polymer chains through C, H-insertion reactions,7,17−24. In such reactions the cross-linking units can be incorporated into the polymer matrix and induce the linking of the involved polymer chains after thermal or UV-activation by (formal) C, H-insertion. Upon imparting heat or light into the film, the cross-linker units can be activated and generate a reactive intermediate, which depending on the chemical nature of cross-linkeris in our case a biradicaloid triplet state7 or a nitrene,24 which then reacts with almost any groups in the neighboring chains through a C, H-insertion reaction (CHic = C, H-insertion based crosslinking). The kinetics of cross-linking of polymers in general is well studied. Since the seminal work of Flory25,26 and deGennes,27 hundreds of papers have dealt with the description of the process of the formation of polymer networks.28 An important concept here is the percolation theory, first developed by Broadbent and Hammersley, who introduced the term in 1957.29 The kinetics of cross-linking in thin films, however, has been addressed less thoroughly. Although the curing of thin coatings is very important from an application point of view, much less attention has been directed to the theoretical description of the process. Most publications focus on the practical aspects under which conditions curing is achieved and under which curing remains incomplete. Received: December 18, 2015 Revised: February 24, 2016

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DOI: 10.1021/acs.macromol.5b02734 Macromolecules XXXX, XXX, XXX−XXX

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Figure 1. (a) Chemical reaction schemes of the cross-linking of polymers containing styrene−sulfonyl azide (SSAz)17 and (b) methacryloyloxybenzophenone (MABP).18 (c) Schematic depiction of the cross-linking process; the empty symbols depict nonactivated and the filled symbols activated groups; the latter lead to the formation of cross-links (blue) or do not contribute to the network (gray). (d) Conversion of the cross-linker units shown in (a) and (b) as a function of time for the thermally activated cross-linker SSAz (PMMA-co-2.5%SSAz, solid line, T = 160 °C) and the UV-activated cross-linker MABP (PS-co-3.6%MABP, dashed line, λ = 365 nm, I ≈ 2.2 mW/cm2). (e) Gel content of polymer films obtained through the same reactions as in (c) for PMMA-co-2.5%SSAz (solid line, T = 160 °C) and PS-co-3.6%MABP (dashed line, λ = 365 nm, I ≈ 2.2 mW/cm2). solution of 3-ethoxybenzophenonsilane in toluene (50 mmol/L), and spin coated at 600 rpm for 60 s (Delta 6RC, Süss Microtec, Germany). After this the sample was heated to 120 °C for 30 min on a hot plate to promote attachment of the silane to the wafer surface. After extraction with toluene and blow-drying, the wafer was cut into samples having a size of approximately 2.5 cm × 1.5 cm. PMMA-co2.5%SSAz (Mn: 117 kg/mol; Mw: 284 kg/mol) and PS-co-3.6%MABP (Mn: 81 kg/mol; Mw: 178 kg/mol) were dissolved in toluene (20 mg/ mL). The samples were immersed into the solution and withdrawn with a pulling speed of 100 mm/min (PMMA-co-2.5%SSAz) and 80 mm/min (PS-co-3.6%MABP). Afterward, transmission FT-IR spectra (Excalibur 3000, Bio-Rad, USA) of the SSAz samples were recorded as a reference to the later collected spectra after heating. Then the samples were heated at 160 °C and irradiated with UV light (λ = 365 nm, I ≈ 2.2 mW/cm2, Stratalinker 2400 from Stratagene, USA) for the given times to initiate cross-linking and surface attachment. After this procedure the initial layer thickness was determined by using ellipsometry (Nanofilm EP3, Accurion, Germany) as well as the decay of the SSAz by FT-IR. The samples were then carefully washed with toluene in a Soxhlet apparatus overnight and blow-dried. Afterward, the samples were dried on a hot plate at 60 °C for 20 min to remove any solvent left in the layers, and the layer thickness

In previously described experiments we observed that the kinetics of the activation of the cross-linking units and the development of the gel content as a function of time do not correspond to each other and are correlated with each other in a strongly nonlinear fashion (see Figure 1c,d; note the different time scales). For some experiments an induction period was observed where film growth was very slow, followed by a rapid rise of the gel content. In other samples the cross-linking was surprisingly fast; even after very low conversion of cross-linker the film was completely linked to the surface, and no more sol component could be extracted. In this paper we investigate the kinetics of cross-linking in deposited thin films by C, Hinsertion reactions from an experimental point of view and compare this to a simple description of the gelation process using percolation theory.

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EXPERIMENTAL SECTION

Relation between Rate of the Activation of the CrossLinking Units and Gel Content. A double-sided polished silicon wafer was cleaned with isopropanol and toluene, fully covered with a B


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as the quotient of the thickness of the as-deposited film h0 and the thickness of the polymer layer after extraction h:

was again measured by ellipsometry. The kinectics of the activation of the incorporated MABP units was recorded separately. Quartz slides were cleaned with ethanol. A PMMA-co-10%MABP (Mn: 149 kg/mol; Mw: 295 kg/mol) solution in toluene (40 mg/mL) was spin coated at 1500 rpm for 30 s (Delta 6RC, Süss Microtec, Germany). UV−vis spectra (Cary 50 Bio, Varian, USA) were recorded and compared to the ones after UV illumination for the given times. Photochemical Cross-Linking. Quartz slides were cleaned with ethanol and toluene and silanized as described above. A highly concentrated PMMA-co-1%MABP (Mn: 126 kg/mol; Mw: 208 kg/ mol) solution in toluene (286 mg/mL) was spin coated onto the substrate (2000 rpm, 60 s) to generate layers in the micrometer range. To obtain thinner layers, the solution was diluted with toluene and additional substrates were coated in the same way. Afterward, the samples were placed on a hot plate at 60 °C for 10 min to evaporate any solvent left in the layer. The samples were covered with a stripe mask and cross-linked by UV irradiation with a dose of 50 mJ/cm2 at 250 nm using a Stratalinker 2400 (Stratagene, USA). For the illumination from the top the polymer layer was covered by an additional quartz slide to ensure the same conditions as for the illumination through the substrate. Additionally, on each sample one extra stripe was irradiated with a dose of 1000 mJ/cm2 as a reference to be able to determine the initial layer thickness. In total, there were three stripes on each sample: one reference, one illuminated from the top, and one illuminated through the substrate. After that the samples were extracted with toluene in a Soxhlet apparatus overnight and dried. The thickness measurements were carried out with a mechanical profilometer (Dektak 150, Veeco, USA). Simulations. All simulations were performed using Mathematica 9.0.1 (Wolfram Research, Champaign, IL) on a 2D lattice with 250 grid points in each direction. The grid points were occupied with the help of a random generator with respect to a particular occupation probability p determined by the rate constant k. For the calculation of the gel content (i.e., strength of the percolating cluster) induced by UV cross-linking, the light absorption of the layer and therefore the intensity profile of the light throughout the film needs to be considered. The absorption coefficient was set to α = 20 cm−1, and each row represents a layer with a thickness of 1 μm.

g = h / h0

(1)

In this respect the cross-linking in (extracted) thin films is very different from conventional cross-linking systems, as only clusters of polymer chains attached to the surface make a contribution to formation of the coating and all others are removed, irrespective of how large they are. In order to calculate the gel content as a function of conversion of the cross-linker units and the film thickness of the initially deposited film, we use the percolation theory on a Bethe lattice, which can be solved exactly.30 In this model all chains that are linked together are represented by clusters in such a way that the more chains are linked together, the larger the cluster becomes. This allows the determination of the time and thus conversion when an infinite (percolating) cluster is obtained, i.e., a cluster which spans the whole film. Additionally, it allows calculating how many sites/chains become attached to the surface during heating or light irradiation. According to this, the probability that a site, which represents in our case a polymer chain, is connected to the infinite cluster is P(p) = p(1 − Q z)

(2)

with the probability p that a certain site/bond is occupied, the number of branches per site z which represents the number of cross-linking units per polymer chain and the probability that a site/bond is not connected to the infinite cluster Q (p) = (1 − p) + pQ z

(3)

Note that the exponent in these equations is z instead of the usual z − 1 in standard percolation theory because the C, Hinsertion is a first-order reaction and no second reaction partner is required. However, this difference is of little importance in the study reported here, as z is in the samples described here approximately 30, i.e., z ≫ 1. We can use these two equations to describe the strength of the percolating cluster as a function of time t. To do this we need to calculate the parameter Q by using the probability of having an activation/decay of at least one cross-linking unit p. This can be calculated from the respective reaction rate constant, which is obtained from the FT-IR measurements, and the number z of groups contained in the polymer:

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RESULTS The C, H-insertion cross-linking reactions are performed by using copolymers containing repeat units consisting of the thermally active styrene−sulfonyl azide (SSAz)17 or the photochemically active methacryloyloxybenzophenone (MABP)18 incorporated into the polymer (Figure 1a). In the former case thermal activation leads to the cleaving off of nitrogen and formation of a nitrene, which can insert into almost any C−H bond, leading to the formation of a stable sulfonyl amide. In the latter case UV irradiation leads to formation of a biradicaloid triplet state, followed by abstraction of a hydrogen atom and recombination of the formed carboncentered radicals. As a result of the activation of the cross-linker units first two, and with increasing reaction progress more and more, polymer chains are connected to each other. Upon reaching a critical number of such links gelation in the layer occurs. Such a process can be described by standard percolation theory. As a result of the activation processes polymer chains are linked to each other and formin the picture of percolation theorya (finite) cluster of polymer chains. When such clusters are attached to the surface of the substrate, they cannot be washed away during extraction. Clusters, however, not covalently linked to the substrate this way are completely removed during extraction. The more clusters are attached to the surface and the larger they are, the higher the final film thickness after extraction h will be. In the following the gel content g is defined

Q−1 = p = 1 − e−zkt Qz − 1

(4)

This equation gives one (real and positive) solution for Q so that the strength of the percolating cluster as a function of time t can be calculated according to P(t ) = (1 − e−zkt )(1 − Q z)

(5)

As z is a relatively large number this converges to

P(t ) = 1 − e−zkt

(6)

Additionally, it has to be taken into account that the calculation of the percolating cluster is only meaningful once the percolation threshold pc is reached. This occurs after the critical time tc; i.e., in the calculations only times t > tc must be considered: C


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Table 1. Rate Constant of the Activation of the Azide Groups in PMMA-co-2.5%SSAz as a Function of Temperature

⎪

⎪

(7)

The percolation threshold pc marks the establishment of an infinite network throughout the polymer layer, which means that a continuous path from one end of the film to the other is formed.25 This is achieved as soon as on average one crosslinking unit per polymer chain has successfully made a connection to a neighboring chain. Therefore, we define for our case of C, H-insertion cross-linking: pc = 1/z = 1 − e(−ktc)

temp [°C]

rate const k [min−1]

temp [°C]

rate const k [min−1]

140 150 160

0.008 0.018 0.042

170 180

0.105 0.269

(8)

Note that eq 8 considers only the cross-linking units and their kinetics and not the complete polymer chain. Finally we obtain P(t ) = 1 − e−zk(t − tc)

(9)

For the latter considerations we have to introduce a parameter j, the efficiency factor, because not every cross-linking unit, which has been activated, contributes to the process which generates the percolating cluster. There is the possibility that a cross-linking unit links to its own chain and builds a loop or that it reacts in a side reaction that does not lead to a cross-link. This parameter j can be taken out of a gel content graph by identifying the time of the percolation threshold tc or by fitting the experimental graph with eq 10 with j as adjustable parameter: P(t ) = 1 − e−jzk(t − tc)

Figure 2. Calculated gel content according to eq 9 as a function of reaction time for different values of the cross-linker contents z (▲: z = 4; ●: z = 6; ⧫: z = 10; ★: z = 30). The reaction rate of the thermal activation process was k = 0.00 min−1, which corresponds to a crosslinking temperature of T = 140 °C.

(10)

This converts also eq 8 into pc = 1/(jz) = 1 − e(−ktc)

(11)

The average number of cross-linker units contained in one polymer chain z can be calculated from the molar fraction of incorporated cross-linker x and the molecular weight of the polymer according to z = xM n /((1 − x)M 0 + xMc)

(12)

where M0 represents the molecular weight of the matrix repeat unit, Mc the molecular weight of the cross-linker repeat unit, and Mn the number-average molecular weight of the polymer. This means that the PMMA-co-2.5%SSAz polymer (Mn: 117 kg/mol) contains approximately 28 SSAz units per polymer chain, the PS-co-3.6%MABP (Mn: 81 kg/mol) has around 27 MABP units per polymer chain incorporated, and the also used PMMA-co-9%SSAz polymer (Mn: 85 kg/mol) contains approximately 70 SSAz units. Thermal Cross-Linking. For a thermally induced crosslinking process the rate of conversion of the cross-linker can be obtained from the decrease of the azide absorption band in the FT-IR spectrum. From these analyses we obtain the rate constants k given in Table 1. From this the gel content as a function of time of such a cross-linking process can be calculated using eq 9. Figure 2 shows the calculated gel content over time for different values for z. When now the Bethe lattice calculations are compared to the measured gel contents of the layers, it is seen that qualitatively the theoretical description is in agreement with the film thickness measurements on such (extracted) films (Figure 3). In the experiments for a high conversion of cross-linker units,

Figure 3. Simulations on a Bethe lattice (dashed lines, calculated by using eqs 8 and 9) and experimental results (solid lines) for the gel content as a function of time. (a) PMMA-co-2.5%SSAz at T = 160 °C; layer thickness: ca. 150 nm; simulation with z = 28 and k = 0.04 min−1. (b) PMMA-co-9%SSAz at T = 120 °C;31 layer thickness: ca. 130 nm; simulation parameters z = 70; k = 0.000 72 min−1.

i.e., high values of z and high reaction rate, a very rapid increase of the gel contents is observed, and only very little of the initially deposited polymer can be washed away. This increase can be so very strong that the time resolution of the experiment D


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cross-linking reaction is set as z = 4. The nonreacted polymer chains are depicted in white, polymer chains, which have been linked to another chain, in gray, and chains, which have been linked to the substrate, in black. It is seen that in the beginning of the cross-linking reaction the number of chains, which are attached to the surface of the substrate, increases only very slowly. At a certain point, the gel point, an infinite cluster is formed, which spans the whole film and gives rise to a rapid increase of the gel content of the layer. However, at this stage, the polymer layer still contains many finite size clusters, which form a sol component. As the reaction proceeds, the sol component becomes smaller and smaller until the cross-linking process is complete. UV Cross-Linking. In the case of UV-activated cross-linking it should be noted that, in addition to the discussions above, the intensity of the incoming light is not constant throughout the film but that the light intensity I(d) decreases from an initial value I0 with increasing depth of the polymer layer according to Lambert−Beer’s law I(d) = I0e−αd, where I is the intensity, d is the distance from the surface where the light enters the film, and α is the linear absorption coefficient, the product of the concentration c of the chromophores in the film and the molar absorption coefficient ε of these chromophores. The conversion p of the cross-linker units z depends on I(d) and the quantum efficiency Q, so that p(d) = QI0e−αd(1 − e−kt )

(13)

It should be noted that the quantum efficiency Q describes the fraction of photons which lead to the desired chemical reaction in relation to those, which have been absorbed. It is to some extent similar to the parameter j above, but also includes radiation and radiationless losses not leading to a chemical reaction. The reaction rate constant k depends now on the light intensity, the wavelength (i.e., energy) of the incoming light, and the absorption spectrum of the cross-linker. The UV cross-linking behavior thus differs from thermal cross-linking strongly in that respect that the conversion of the cross-linker is not the same throughout the film but varies locally very strongly. This leads to a situation that the gelation behavior of the layer in the horizontal plane is different from that in the vertical direction, and in some cases gelation can occur in the horizontal plane, while orthogonally to the surface the gel point is not reached. Additionally, for light-induced cross-linking two cases need to be distinguished: one where the sample is irradiated through the (transparent) substrate and one where the sample is irradiated from the far side with respect to the substrate. If we now start with looking at the film irradiated from the top and view the film as a series of thin slices parallel to the surface, it is obvious that the light intensity and thus the conversion decrease exponentially with the distance from the surface. Thus, each plane reaches the gel point at a characteristic time given by the distance from the surface, the initial light intensity or more precisely the light dose, the absorption coefficient, and the number of cross-linking units per chain. During irradiation the percolating clusters grow from the top through the polymer layer until it reaches and reacts with a cluster with connection to the substrate an infinite network also in the direction orthogonal to the surface is formed (Figure 6). However, if the photoprocess is stopped before the infinite network is reached in this direction, practically all of the material is washed away during extraction of the film, and only

Figure 4. Experimental results (solid lines) and fits (dashed lines, according to eq 10) for the gel content of as a function of time. (a) PMMA-co-2.5%SSAz at T = 160 °C layer thickness: ca. 150 nm; fit with z = 28, k = 0.04 min−1, j = 1.27 ± 0.15. (b) PMMA-co-9%SSAz at T = 120 °C,31 layer thickness: ca. 130 nm; fit with z = 70; k = 0.000 72 min−1, j = 0.59 ± 0.03.

However, the situation on a Bethe lattice with high values of z becomes difficult to visualize even after very short times. Accordingly, a similar calculation was performed on a 2D lattice (grid size 250 × 250) to illustrate the situation. In Figure 5 such a reaction with a rate constant of k = 0.00 min−1 is shown. In the depicted simulations the product of the number of crosslinker units contained in the copolymer, and the yield of the E


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Figure 5. Visualization of the thermal cross-linking behavior of a polymer layer as a function of time respectively conversion of the cross-linker units for T = 140 °C (z = 4, k = 0.00 min−1) at (a) 2, (b) 74, (c) 111, (d) 119, (e) 121, and (f) 129 min. Unreacted sites/polymer chains are depicted in white, polymer chains linked together in gray and polymer chains connected to the substrate in black; lattice size: 250 × 250 each grid point represents a polymer chain.

Figure 6. UV-activated cross-linking of a polymer layer as a function of irradiation time with a rate constant k = 0.5 min−1 as determined from spectroscopic measurements. The number of cross-linking units z was z = 4, and the absorption coefficient was 20 cm−1. Un-cross-linked sites/ polymer chains are depicted in white, polymer chains linked together and forming small clusters in gray, and polymer chains with connection to the upper or lower surface in black. The times of illumination are 0.2 (a), 1.3 (b), 2 (c), 2.7 (d), 3.8 (e), and 4.7 min (f).

When the situation is studied where the illumination is carried out from the top, three different regimes can be identified (Figure 7a). The exact values of the transitions

some small clusters which are already bound to the surface remain. F


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the surface; only occasionally some shreds of a cross-linked material remain after extraction. This situation is depicted in the calculations shown in Figure 6e,f, where in one situation the percolating cluster does not reach the surface, while in the other situation it does. If the illumination of the polymer layer is performed through the substrate, quite different results are obtained (Figure 7b,c). Here (for a given light dose) the thickness after extraction increases linearly with the thickness of the as-deposited layer, indicating complete cross-linking. However, when the thicknesses of the deposited layers reach a critical value, which is for the given dose at about d0 ≈ 1900 nm, this increase in layer thickness levels off and at high thicknesses of the as-deposited layers a constant film thickness is obtained (Figure 7b). Accordingly, when the gel contents of the layer are plotted as a function of the initial layer thickness, a linear decrease is observed (Figure 7c).

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DISCUSSION The kinetics of the formation of surface-attached polymer networks via C, H-insertion reactions can be well understood using simple considerations based on percolation theory. For these it must be taken into account that in copolymers such as the ones described here the number of cross-linkable units per chain is very high (in the polymers studied here around 30 and 70 groups per chain). This leads to a situation where already rather small conversions of the cross-linker lead to complete cross-linking of the layer. To estimate the number of active links between polymer chains forming the gel, an efficiency factor must be taken into account, which accounts for the fact that some activated groups do not react in such a way that a cross-link is formed, but side reactions (e.g., loop formation) occur. In contrast to conventional cross-linking mechanisms based on the reaction of two reactive groups on the polymer for C, H-insertion based cross-linking (CHic) reactions, the “active” binding of cross-linker groups with neighboring polymer chains is not the only process which contributes to the formation of a cross-link. Even chains which carry no crosslinker units at all can be incorporated into the forming network simply by the fact that a neighboring chain attacks it successfully through C, H-insertion and binds it to the network (“passive binding”). According to the percolation model of gelation, the gel content g, i.e., how much of a physically deposited film is converted into a surface-attached network during a thermally or photochemically induced cross-linking reaction, depends on whether an infinite, percolating cluster of covalently linked polymer chains is formed and connected to the surface in the process. If this is not the case, most of the material can be washed away during solvent extraction (Figure 5a−e). Only finite clusters, which are by coincidence so close to the surface that some part of it forms a covalent link to a surface group, will be bound. This leads to a period of rather slow growth of the polymer layer (Figure 3b). However, once a critical conversion of the cross-linker units is reached, an infinite cluster of interlinked chains is formed. Thus, at the percolation threshold the layer thickness after cross-linking and extraction increases rather strongly (Figure 3b). Because of the high number of functional groups present in the polymers and the possibility of active and passive binding, the infinite percolating clusters can be already obtained at rather low conversion of the cross-linker. This can be indeed so very low that already at the first data points almost full conversion is obtained (Figure 3a).

Figure 7. (a) Gel contents of PMMA-co-1%MABP films after illumination from the top. (b) Layer thickness after extraction h over layer thickness before extraction h0 of the same polymer film illuminated through the substrate (λ = 250 nm, 50 mJ/cm2). (c) Graph of the gel content of (b). The solid lines are only guide to the eye and do not represent fits to the data. No implications are made about the sharpness of the transitions between the individual regimes.

between the regimes depend on the dose used in the irradiation experiments, which is set to 50 mJ/cm2 in the following. One of these regimes occurs at thicknesses of the as deposited films d0 of d0 < 1900 nm. For this dose all polymer is cross-linked and covalently attached to the surface, so that in all cases a gel contents of g = 1 is obtained. The films are as smooth as the initially deposited layers (Figure 8, left). This is followed by a second regime, which is at 1900 nm < d0 < 3000 nm for the given light dose. In this regime, the films obtained after crosslinking and extraction are strongly heterogeneous (Figure 8, right), and the layer thicknesses of the surface attached networks are difficult to reproduce. In the third regime, at film thickness d0 higher 3000 nm, no polymer becomes attached to G


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Figure 8. Surface profile maps of PMMA-co-1%MABP films after illumination (λ = 250 nm, 50 mJ/cm2) from the top and extraction with toluene. Left: sample of region I. Right: sample of region II.

During thermally induced cross-linking, functional groups throughout the whole polymer film become activated and the process occurs more or less in a homogeneous way. In contrast to this, the energy imparted into the film during photochemical cross-linking decreases exponentially with increasing distance from the surface. Due to the progress of the photochemical reaction, the light absorption, however, decreases with time as more and more chromophores become consumed during the photochemical reaction. Additionally, the infinite, percolating cluster grows from the side of the film facing the UV-light. This means that if the film is illuminated through the substrate, with increasing illumination time the light penetrates deeper into the film. When the illumination time and thus, at a given intensity, the dose imparted into the film are fixed and films of varying initial film thickness are viewed, this means that up to a critical thickness of the as-deposited film practically all material becomes attached and the thickness of the gel layer increases linearly with the as deposited film thickness (Figure 7b). However, when the thickness of the as-deposited film is higher than this critical film thickness, the conversion of the crosslinker becomes lower and lower with increasing distance from the surface. Beyond a certain distance from the surface the conversion becomes so very low that it drops below the percolation threshold, and all polymer present in such locations is washed away in a following extraction process (Figure 7c). As a result of this, the thickness of the obtained surface-attached network becomes independent from the fact of how much polymer was deposited initially. Under this circumstance the maximum obtainable thickness for a given system depends only on the dose of the UV-light employed in the irradiation process. The situation is, however, quite different if the illumination occurs from the other side, i.e., from the far side of the film with respect to the substrate surface. The exponential decay of the intensity of the incoming light with increasing depth leads to a situation which can be described by three scenarios (Figure 7a): In the first scenario the film thickness is so low that throughout the whole film the dose of the UV light and thus the conversion of the cross-linker are high enough, so that the percolation threshold is reached even at the far side of the film in respect to the incoming UV-light. In this case all polymer which has been deposited is rapidly cross-linked and attached to the surface, and a very homogeneous surface-attached network layer is obtained (Figure 7a, I). In a second scenario (Figure 7a, III) the film thickness is so high (and/or the dose of the light is so low)

From a principle point of view the establishment of only one chemical bond or a few bonds connecting the cluster and the surface (or in terms of percolation theory, one critical path) would be sufficient to anchor the cluster to the surface and thus contribute to the surface-attached film. However, mechanical forces acting onto such a large cluster of polymer chains during the extraction process might be sufficient to break this bond or these bonds and lead to the breaking off of this cluster and thus to an at least partial removal of the film. Only when a sufficient number of connections are established the film becomes mechanically stable. Thus, the thicknesses of the layers in this regime are more difficult to reproduce, and frequently rather rough layers are obtained very close to the gel point. However, once this regime is surpassed, the attachment process becomes extremely robust and smooth and completely cross-linked layers are obtained. It is important to note that the cross-linking kinetics appears to be in some cases faster (Figure 3a) and in some cases slower (Figure 3b) than expected by simple percolation considerations. The reason for this could be a deviation of the efficiency of the attachment reaction from unity. The efficiency of the cross-linking reaction comprises two phenomena which occur during the gel formation. The first one takes into account that not every cross-linking unit reacts as desired but might form a loop or could undergo a side reaction. This is taken into account by introducing an efficiency factor j, which in this case assumes a value between 0 and 1. The second phenomenon is that during formation of an infinite cluster immediately such an infinite cluster entraps many smaller, finite clusters. These are from a principle point of view, part of the sol component, but can be so firmly trapped inside of the film that they cannot be washed out during extraction. To understand this, it must be considered that even when only a few of the polymer molecules are linked together, the size of such a branched cluster is quite considerable due to the high molecular weight of the employed polymers and will quickly reach values of millions of gram/mol. Accordingly, the time frame required for such molecules to reptate through the network in order to be washed out will be very high. Because of these entrapped chains, the polymer films contain more chains than expected by percolation theory. The parameter j increases and can in some cases even lead to values of j > 1. These two opposing factors both contribute to the value of the parameter j, albeit with differing weight. The relevance of the two factors might even change in the course of the reaction. H


Article

Macromolecules

cross-linker conversion varies between different locations in the film as the polymer absorbs light. Therefore, situations can occur in which in some areas of the film the percolation threshold is reached, while in others this is not the case. This can lead to a situation that, despite complete cross-linking in some part of the film, still complete film removal occurs during extraction because close to the substrate surface the percolation point is not reached and the formed network does not become linked to the substrate. The developed model allows, with only one adaptable (a priori unknown) parameter, namely the efficiency factor j, the prediction of the complete cross-linking behavior of CHic based cross-linking reactions and thus facilitate to use this very simple and versatile method to generate tailor-made surfaces.

that the gel point is not reached in the layer directly adjacent to the surface. In this case the forming network does not become attached to the substrate and is washed away during extraction. In a third regime located between the two others (Figure 7a, II) the deposited polymer layer thickness is close to the critical value which separates the two regimes described above. In this case, as described above, the mechanical forces during extraction of the layer lead to complete or partial destruction of the film. Eventually, only smaller or larger shreds of the film remain attached so that a strongly inhomogeneous layer results and a strong scattering of the thicknesses of the network is observed (Figure 8, right). All these factors contribute to the fact that during C, Hinsertion based cross-linking (CHic) reactions a very strongly nonlinear relation between the number of activated cross-linker units and the final layer thickness of the surface-attached gel layer is observed. While the activation of the cross-linkers follows a first-order kinetics, the formation of surface-attached network layers follows a kinetics involving a short induction period with low thickness increase, followed by a very rapid increase and eventually a leveling off at high gel contents. The increase, however, might be so strong and so very fast that already at the first measurement carried out after very brief irradiation or brief heating the network formation is almost complete, and more or less all of the film is transformed into a gel. Only when the conversion of the cross-linker is rather slow and/or the efficiency factor of the cross-linking process is not very high this induction period is visible.

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AUTHOR INFORMATION

Corresponding Author

*E-mail [email protected] (J.R.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We want to thank Malwina Paschek for supplying polymer materials, Vanessa Weiss for measurements of the cross-linking kinetics, and the Deutsche Forschungsgesellschaft (DFG) for funding this project within the Collaborative Research Center “Transregio 123 - Planar Optronic Systems”.

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CONCLUSIONS The cross-linking behavior of polymers via CHic based formation of surface-attached polymer networks is in some respect very similar to conventional gelation processes in the bulk and in other aspects not. A simple percolation model allows the prediction of the formation of surface-attached polymer networks of such polymers as a function of reaction time and reaction conditions. It allows the connection of the kinetics of the thermal or UV induced activation of cross-linker units with the amount of polymer deposited after irradiation/ thermal treatment and extraction. The percolation model also allows one to predict the cross-linking behavior of deposited thin films of the polymers from known parameters, such as the kinetics of the activation of the cross-linker, cross-linker contents, molecular weight, film thickness, temperature or light dose, and absorption coefficient. The relatively large number of cross-linker units per polymer chain and the entrapment of finite cluster into the surface-attached infinite cluster explains why the process of thin film formation by such cross-linking reactions is under many circumstances surprisingly rapid and why under other conditions an induction period is observed after which rapid film growth occurs. Some aspects of the cross-linking process are unique for this way of layer generation. First, all clusters which do not become covalently attached to the surface are washed away during extraction, so that the layer growth below the percolation point is slow and not directly correlated to the conversion of the cross-linker units. Second, sol components consisting of high molecular weight components where the clusters are large but still soluble canfrom a principle point of viewbe washed away during extraction. However, they are so very large, that they become entrapped in the film. They cannot be washed out and contribute to the layer, even though they are not part of the network. Third, intrinsically to all photochemical processes the

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