Article pubs.acs.org/Macromolecules
Surface Microdynamics Phase Transition and Internal Structure of High-Density, Ultrathin PHEMA‑b‑PNIPAM Diblock Copolymer Brushes on Silicone Rubber K. Jalili,†,‡ F. Abbasi,*,† and A. Milchev‡,§ †
Institute of Polymeric Materials, Sahand University of Technology, Tabriz, Iran Max Planck Institute for Polymer Research, Ackermannweg 10, 55128 Mainz, Germany § Institute for Physical Chemistry, Bulgarian Academy of Sciences, 1113 Sofia, Bulgaria ‡
S Supporting Information *
ABSTRACT: Stimuli-responsive ultrathin diblock copolymer brushes (DCBs) composed of poly(2-hydroxyethyl methacrylate) (PHEMA) as bottom block and poly(N-isopropylacrylamide) (PNIPAM) as top block on the surface of silicone rubber (SR) were examined as high-throughput platforms to trace the thermally induced phase transition mechanisms in water. A high grafting density DCB was precisely prepared from SiOx substrate via surface-initiated atom transfer radical polymerization (SI-ATRP). Surface modification studies with different initiator concentrations were performed to optimize their attachment, producing surfaces with dense covalently attached initiator monolayers with up to 2.8 initiators/nm2. Changes in the physicochemical properties according to each step of surface modification were investigated using in situ analysis with the sample both in a liquid environment and on layer in dry state. The temperature-dependent contact angle of the air bubbles underneath the high-density DCB (0.53 chains/nm2) gradually increased up to around 24 °C in water with increasing temperature and then decreased up to around 30 °C, followed by a rapid decrease at LCST of PNIPAM top block, approximately 32 °C. To obtain a thorough understanding of the microdomain orientation in DCB, the structure of SR/PHEMA-b-PNIPAM brush was investigated by μ-focused grazing incidence small-angle X-ray scattering (μ-GISAXS). Upon exposure to higher temperature conditions (above the LCST of PNIPAM top block), the film showed a “matrix-island” structure, in which the PNIPAM nanodomains were distributed over the highly packed PHEMA bottom block. The thermally induced evolution mechanism of various interactions in PHEMA-b-PNIPAM DCB and water mixtures during the heating−cooling cycles was investigated by means of temperature-dependent FTIR in combination with a two-dimensional correlation (2Dcos) technique. Both conventional IR spectrum and 2Dcos had figured out the volume phase transition temperature for PNIPAM top block and PHEMA bottom block to be about 33 and 33.5 °C, respectively, close to the results obtained from turbidity measurements [Sun et al. Sof t Matter 2013, 9, 1807; Weaver et al. Macromolecules 2004, 37, 2395] on the same bulk polymers.
I. INTRODUCTION Polymer brushes chemically tethered to the surface at one end leaving the other free possess well-defined architectures that can be analyzed more easily than other more complex structures, such as those obtained by plasma graft polymerization or layer-by-layer polymerizations.1,2 Brushes of stimuliresponsive polymers have garnered attention, due in part to their particularly to surface property tuning especially when they are submitted to external stimuli such as temperature,3−5 light,6−9 ultrasound,10 electromagnetic fields,11−13 and changes in the pH and ionic strength14−18 of the environment. Of the various brush compositions that include homopolymer, block copolymer, and random copolymer, diblock copolymer brushes (DCBs) have received increasing attention because of their reversible responsive properties that are possible depending on surface morphology, block length ratios, and interactions © 2013 American Chemical Society
between the two blocks relative to each other and with the local environment.19−29 The main difference between these brushes and binary mixed homopolymer brushes is that the phase domain structure is usually well ordered and periodic, allowing them to be useful in applications of nanopatterning and templates.30,31 Zhao et al.32−34 showed for the first time that the surface of a PS-b-PMMA brush can be rearranged by changing the character of the solvent contacting the brush before it is dried. Most of the studies regarding the multiblock copolymer brushes demonstrated that the surface rearrangement could be observed with a variety of block combinations in various solvents, but none of them explained how the surface Received: February 24, 2013 Revised: May 9, 2013 Published: June 25, 2013 5260
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rearrangement occurs. Zhao et al.32 conjectured what the internal structures of the brush films might be in the “asdeposited” and “switched states”, but they did not confirm the internal structure since it could not be resolved with their techniques. The average spacing between grafted polymer chains scales inversely with the grafting density (Σ), the number chain per area.2 This parameter affects the conformation of the polymer chain in the grafted layer. As Σ increases, polymer chains get closer together and begin to overlap, increasing the excluded volume and causing chains to extend farther from the substrate. The behavior of grafted chains as a function of the grafting density (in solvents with various qualities) has been addressed in a number of theoretical studies.35−40 The scaling behavior in solution can generally be described as H ∝ N Σn
mentioning that by LeMieux et al.,48 where the nanomechanical response of stratified polymer brush was studied using AFM nanoindentation test on silicon covered with PNIPAM-b-PBA DCBs. The strong characteristic LCST behavior of PNIPAM was observed in water, with a 100% change in thickness above and below this transition. Their AFM nanomechanical results demonstrated vertical gradients of the elastic response tunable to a desired state by the external temperature. There is indeed a lack of knowledge of how the change in hydration state during the coil−globule transition of the DCBs involving PNIPAM block can affect the microdynamic phase transition mechanism of PNIPAM chains in aqueous solution. Understanding the revival thermodynamics of chain collapse of PNIPAM in its DCB state in relation to their nanoscale organization is extremely important for the design of surfaces and devices with tailored properties as barrier or protecting coatings. Moreover, in the case of PNIPAM involved DCBs, it is not clear how the thermally induced collapse transition affects molecular transport through the brush and its blocking character of the modified surface, respectively. The analytical methods and devices, which can improve analytical efficiency and throughput, especially in the medical diagnostics, genomics and proteomics, are greatly desirable.49,50 Microfluidic devices have attracted increasing attention since the 1990s, as they have high sample throughput, low consumption of sample and reagents, and automatic control.51−53 Recently, a variety of polymeric materials have been increasingly adopted in producing various microfluidic devices.54−58 One of these biomaterials, silicone rubber (SR), is widely known as an appropriate material not only for surface patterning and topographic modification but also as a good substrate for cell growth, proliferation, positioning, and differentiation owing to a number of advantages: simple fabrication by replica molding, biocompatibility, nontoxicity, excellent optical transparency down to 280 nm, and permeability to gases.59−61 In spite of these advantages, the strong hydrophobicity of SR surface always impedes SR-based microfluidic devices from immediate use without any surface processing. The key challenge is the surface fouling problem caused by protein or analyte adsorption on hydrophobic surface enhanced by significant increase in surface-to-volume ratio in microscale, resulting in low device performance and substantial sample loss. Therefore, it is of key importance to develop efficient surface modification techniques to render SR surface protein resistance. To address these issues, we have synthesized well-defined and precise controlled ultrathin thermoresponsive DCB composed of poly(2-hydroxyethyl methacrylate) (PHEMA) and PNIPAM at high grafting density via surface-initiated atom transfer radical polymerization (SI-ATRP) on SR surface and studied its physicochemical properties, which are distinct from those of past sparsely and roughly grafted PNIPAM homo- and copolymer brushes. X-ray photoelectron spectroscopy (XPS) and grazing angle attenuated total reflectance Fourier transform infrared (GATR-FTIR) spectroscopy were used to analyze surface compositions of the silanized SR substrates and substrates grafted with polymers. We investigated the switching behavior of the SR-based DCBs using in situ measurements over a wide range of temperatures. The change in structure between the equilibrium states was investigated by X-ray reflectivity (XRR), atomic force microscopy (AFM), water and air bubble contact angle measurements, and μ-focused grazing incidence small-angle X-ray scattering (μ-GISAXS). In this
(1.1)
where H is the average extended length of the polymer chain (layer thickness), N is the degree of polymerization, and n is an exponent between 0 and 1. Theoretical studies suggest that the exponent n is a function of both the solvent quality35−39 and the grafting density.35−40 Grafted polymer layers swollen in a solvent are generally grouped into two regimes delineated by a critical chain spacing equivalent to the radius of gyration (Rg) for the free polymer in the same solvent. When chains are grafted at distances larger than Rg, the chains do not interact and the layer behaves similarly to a free polymer. The layer thickness is independent of the grafting density (n = 0) and has a constant value of ∼2Rg in the swollen state. This has been demonstrated both theoretically and experimentally by a number of groups.35−37,41,42 Grafted chains spaced closer than Rg interact with one another, resulting in conformational extensions greater than 2Rg; this regime is known as polymer brush. Early calculations and experimental investigations revealed an n = 1/3 scaling law dependence for brushes swollen in a good solvent,35−38,42 but more recent calculations suggest that at higher grafting densities (Σ > 0.3 nm−2) this increases to as large as n = 1, due to higher order interaction parameters.37−40,43,44 Among the thermally responsive macromolecules, poly(Nisopropylacrylamide) (PNIPAM) is the most popular and wellinvestigated temperature-responsive polymer; this is largely due to it exhibits phase transition in aqueous environments in a narrow temperature range within the tolerances of human metabolism (∼32 °C).45,46 This is due primarily to the coil-toglobule transition at the critical temperature.47 Above this temperature, called lower critical solution temperature (LCST), the hydrogen bonding between amide groups of PNIPAM and water molecules is broken and replaced by intramolecular hydrogen bonds between amide groups. As a consequence, the polymer becomes more hydrophobic, excluding water. PNIPAM precipitates in solution above the LCST. In a brush, PNIPAM collapses, reducing thickness besides losing water. These phenomena are reversible. Reducing the temperature below the LCST, the polymer dissolves in water again, and the brush recovers its original thickness. Even though a great deal of effort has been devoted to characterize the thermoresponsive structural change of PNIPAM homopolymer brushes, considerably less effort has been put in the characterization of internal structure of PNIPAM chains block during phase transition within DCBs. Among the scarce work dealing with this subject, it is worth 5261
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showed that densely packed monolayers with alkyldimethylsilane derivative were highly hydrophobic, with water contact angles of about 110°.75,76 In contrast, however, the value of contact angle of the water drop for our monolayer composed of BrTMOS reached about 75 ± 0.7°. This difference is not due to kinetic limitations but is inherent to the pretreatment of a SR surface and reaction conditions with the alkyldimethylsilane derivatives. Confirmation of the deposition of the BrTMOS surface attachable ATRP initiator was achieved by XPS (Supporting Information, Figure S4a), AFM (Supporting Information, Figure S4b), thin film X-ray reflectivity analysis (Figure 1),
paper, we aim to trace the thermally induced evolution mechanism of interactions of SR-based PNIPAM involved DCB in aqueous solution and figure out the thermodynamic phase transition mechanism mainly using FTIR spectroscopy. A detailed FTIR analysis of PHEMA bottom block and PNIPAM top block during heating−cooling cycles can help us to get an insight into the molecular behavior of the polymer chains within the DCB and interaction between groups with generalized 2D correlation spectroscopy (2Dcos). 2Dcos, a technique originally proposed by Noda,62−64 enables the investigation of the spectral intensity fluctuation under a disturbing variable which can be temperature,65,66 time,67,68 pH,69 and so on. In addition, 2D spectra can greatly improve the spectral resolution, such as separating overlapped peaks in the 1D spectra and discerning the exact positions of peaks.
II. RESULTS AND DISCUSSION Recent developments in the living radical polymerization (LRP) technique, namely ATRP, have allowed for the formation of well-defined, narrow PDI polymers with a wide array of architectures by simple, versatile routes. These characteristics lead the ATRP technique to be ideal in the formation of polymer brushes with high grafting densities, uniform thicknesses, and complex architectures. When fabricating a high-density DCB composed of PHEMA as first block and PNIPAM as second block on the not more flatness SR surface, it is important to choose the appropriate surface conditions for attaching both blocks sequentially to one end and the preparatory procedure to obtain a high-density DCB. A. Incorporation of ATRP Initiators onto SR Surface. One of the challenges in preparing surface grafted polymer brushes from a flat surface is to introduce densely tethered ATRP initiators. Different approaches employed to introduce densely tethered ATRP initiators include the Langmuir− Blodgett technique and chemical modification based on the different properties of the substrate.70−74 A number of different chemical structures of surface silanized membranes composed of organosilanes on a silicon wafer, especially for di- and trihydrolyzable organosilanes, can be produced depending on the reaction conditions because these organosilanes can react not only with Si−OH groups on the surface oxide layer but also with each other in the silanized membranes obtained.75 Monohydrolyzable organosilanes are attractive in terms of the reproducibility of surface structures of silanized membranes on a silicon wafer.75,76 However, because the reactions of the alkyldimethylsilane derivatives with only one hydrolyzable group at the solution−solid interface are very slow in the later stages of the reaction, long reaction times are necessary to achieve maximum bonding density. Alkyltrichlorosilanes with long alkyl groups (e.g., 10−25 carbons) have been often used since the long alkyl groups help assemble the molecules on the surface. Trichlorosilanes are very sensitive to moisture and hard to purify. The water content of the trichlorosilane solution needs to be well controlled during the SAM formation. Otherwise, multilayers or cross-linked particles tend to form on the surface.77,78 Here, we used a more stable trimethoxysilane, BrTMOS, for silanization, which is easy to prepare and purify. Although BrTMOS does not have a long alkyl group that was thought to form a better SAM, it will be shown in this work that the assembly of BrTMOS via solution deposition on the SR surface will form a good silane layer, which is sufficient as an initiator to induce the formation of well-defined DCB via ATRP. Some reports using carefully optimized conditions
Figure 1. X-ray reflectivity curves of the monolayer of BrTMOS (a), BrTMOS/PHEMA (b), and BrTMOS/PHEMA-b-PNIPAM at T = 20 °C (c), T = 25 °C (d), LCST temperature (∼32 °C (e), and T = 40 °C (f). Hollow symbols represent the experimental data. Solid lines represent the Parratt fit. The curves are shifted along the vertical axis for improved visualization.
Table 1. Surface Chemical Composition (at. %) of Initiator SAMs on UVO-Activated SR Determined by the Cassie− Baxter Equation initiator concn (mM)
fsurf A (%)
σ (no./nm2)
static water contact angle (deg)
0.05 10
31 80
1.1 2.8
45 ± 0.7 75 ± 0.7
and water contact angle measurements (Table 1). The thin film X-ray reflectivity measurements for the initiator layer yielded a thickness of 1.9 ± 0.2 nm with a roughness of 0.25 nm. The results were in good agreement with the theoretical calculation (2.0 nm) based on the normal bonds angles and lengths and assuming a 10° tilt angle for the initiator chain.79 Immobilization of the ATRP initiator BrTMOS on a UVO-treated SR surface resulted in an increase in static water contact angle from 41° to 75°, and static contact angle of the BrTMOS initiator layers were relatively uniform. Controlling the surface coverage of the immobilized initiator is a prerequisite for tailoring the grafting density of tethered polymers prepared by surface-initiated polymerization. Given that the initiator immobilization reaction with OH substrates is exothermic, the initiator surface coverage should be a function 5262
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were optimized in MIBK, one clearly obtains from Table 1 the surface density of the BrTMOS initiator in MIBK at 80% of mole fraction reaches σ ≈ 2.8 no./nm2, reflecting the attainment of a very densely packed initiator monolayer and a perfect agreement with the value obtained in the case of 3BIDS. While the UVO-treated SR substrates are electrostatically stable in MIBK, we speculate that higher initiator coverages were obtained in the case of SR/BrTMOS due to the less affinity of MIBK for the SR surface as reflected in its lower dielectric constant (ϵMIBK ≈ 13, ϵethanol ≈ 24). In addition, the polycondensation reaction of silanes derivative in MIBK is conducted at a higher reflux temperature, which corresponds to its higher boiling point (TMIBK = 118 °C, Tethanol = 78 °C). More interestingly, though, at 0.05 mM feed composition of BrTMOS the surface density shows a drastic decrease and reaches σ ≈ 1.1 no./nm2, indicating that the OH functionalities are larger in amount and occupy more space than BrTMOS; however, the initiator monolayer is in intermediate packed state. Evidently, as the mole fraction of BrTMOS in feed composition decreases (resulting in a decrease in surface composition of BrTMOS ( fsurf A ) on the SR substrate), the initiator monolayers attain rather low surface densities. This behavior confirms that the extent of initiator immobilization, and hence the surface coverage can be well controlled by the initiator concentration in feed composition. B. Formation of Homopolymer Brushes on SR Substrates via Surface-Initiated ATRP. An illustration of the general synthesis route for formation of homopolymer brushes of HEMA via ATRP and subsequent ATRP polymerization of NIPAM monomer to form SR/PHEMA-b-PNIPAM DCBs is shown in Figure 1. PHEMA brushes were prepared by SI-ATRP on SR modified with BrTMOS using a catalyst system consisting of CuCl, CuBr2, and bipy in a water−methanol mixture at room temperature. The preparation of the homopolymer brush of HEMA monomer was first followed by XRR to verify the proposed mechanism. The obtained reflectivity curves for selected runs are shown in Figure 1. The analysis of the first prepared PHEMA brush yielded a 6.55 nm ultrathin film with a relative low roughness of 0.50 nm after 1 h ATRP of HEMA in dry state, confirming that the surface was smooth. Support for the successful grafting of the polymer brushes is further obtained from XPS, GATR-FTIR spectroscopy, and AFM imaging (see Supporting Information, Figure S5). The conversion of monomer to polymer and GPC traces for each of the aliquot collected from the cleaved PHEMA from the surface are shown in Figure S6. From the measured dry film thickness H using the XRR technique and the molecular weight Mn of cleaved PHEMA chains from the SR surface measured by GPC, the grafting parameters, including grafting density, Σ (chain/nm2) and the average distance between grafting sites, s (nm), were calculated from the data in Figure S6a,b using eqs 2.2 and 2.3:88
of both the immersion time and initiator concentration. Lego et al. showed that a wide range of initiator surface coverage, from 20 to 87%, is possible by systematically increasing the initiator concentration from 0.05 to 10 mM (a maximum surface coverage of ∼90% was obtained by using the neat initiator 4.5 M).80 In our work, the surface coverage of end-functionalized initiator molecules grafted onto the SR surface was evaluated using the Cassie−Baxter equation and related modified equations correlating the surface coverage of small molecules with the measured static contact angle. For our study, the surface was assumed to be a mixture of an organoalkylsilane of surface coverage fsurf A and surface Si−OH (silanol) groups of surface coverage f surf B . The equilibrium contact angle of a chemically heterogeneous surface, θc, can be related to the fractions of different chemical groups in terms of the phenomenological Cassie−Baxter equation and the modified related equations:81 [1 + cos θc]2 = f Asurf [1 + cos θA]2 + f Bsurf [1 + cos θB]2 (2.1)
f Asurf + f Bsurf = 1
where θA is the static water contact angle of a surface when fsurf A = 1 and θB is the static water contact angle of a surface when = 1. In our study, the water contact angle of a surface f surf B covered with a maximum number of hydrophobic small organoalkylsilane molecules, fsurf A = 1, is assumed to be θA = 90 °C,82,83 while the water contact angle against a freshly UVOactivated SR surface containing only saturated OH groups, f surf B = 1, is assumed to be θB = 20 °C as experimentally determined (Supporting Information, Figure S1). The latter is in good agreement with value reported in the literature.84,85 In order to obtain the different surface coverages from ATRP initiator, monolayers of BrTMOS at two varied molar concentrations, 0.05 and 10 mM, were deposited to freshly UVO-activated SR substrates. For these surfaces, the initiator grafting densities (σ, no./ nm2) values were calculated from the amount of grafted initiator (Γ, mg/m2) at 100% molar fraction of BrTMOS (Γ = hρ, where h is the thickness of the initiator layer obtained by XRR measurements and ρ = 1.168 g/cm3 is the density of BrTMOS) and XPS data according to the formula σ = fsurf A ΓNA × 10−21/M, where M = 370.35 g/mol is the molecular weight of BrTMOS. Table 1 shows the surface coverages fsurf A , surface densities, σ (no./nm2), and contact angles determined for the SAM-Br as a function of the solution composition of the BrTMOS from which the monolayers were assembled (feed solution). The increasing amount of ATRP active molecules (BrTMOS) on SAMs with an increasing of initiator concentration in feed solution demonstrates the ability to control the initiator surface coverage. At high initiator concentration (10 mM), the apparent initial reaction rate is much faster than at lower concentrations so that the control of surface coverage over time is unlikely and only high initiator surface coverage (>60%) are feasible. Full monolayer coverage for the frequently used ATRP initiator, 3-(2-bromoisobutyryl)propyl)dimethylethoxysilane (3-BIDS), in ethanol was benchmarked against the maximum surface coverage for a similar sized monofunctional silane− trimethylethoxysilane (TMES) on silica at σ ≈ 2.8 no./nm2.86,87 Moreover, while the conditions to attach the ATRP initiator
Σ=
s=
Hρp Mn
NA
⎛ 4 ⎞1/2 ⎜ ⎟ ⎝ πΣ ⎠
(2.2)
(2.3)
From Gaussian error propagation an estimation of the grafting density error ΔΣ is possible: 5263
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Table 2. Summary of PHEMA Brush Grafting Parameters polymerization time (h)
σ (no./nm2)
H (nm)
Mn/1000
PDI
Σ (chains/ nm2)
ΔΣ (chains/ nm2)
Σ/σ
s (nm)
RF (nm)
s/(2RF)
1 3.5 4.5 5.5 7 11 15 19
2.8 2.8 2.8 2.8 2.8 2.8 2.8 2.8
6.55 29.24 37.11 45.34 58.30 88.15 118.15 130.64
7.33 31.63 41.12 50.13 64.17 96.90 130.12 146.13
1.29 1.28 1.27 1.25 1.23 1.20 1.20 1.19
0.59 0.61 0.60 0.60 0.60 0.60 0.60 0.60
0.093 0.032 0.028 0.027 0.026 0.025 0.025 0.024
0.20 0.21 0.21 0.21 0.21 0.21 0.21 0.21
1.47 1.44 1.46 1.46 1.46 1.46 1.46 1.46
4.61 10.50 11.94 13.81 15.64 19.98 23.84 25.82
0.15 0.06 0.06 0.05 0.04 0.03 0.03 0.02
LXRR (nm)
conformation
± ± ± ± ± ± ± ±
brush brush brush brush brush brush brush brush
12 55 74 95 112 151 182 208
1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0
Figure 2. Preparation of PHEMA-b-PNIPAM diblock copolymer brushes via SI-ATRP from 2-bromotrimethoxysilane functional SAMs on SR surfaces.
ΔΣ =
⎞2 ⎞2 ⎛ Hρp ⎛ ρp NA ΔH ⎟ + ⎜ − 2 NA ΔM n⎟ ⎜ ⎠ ⎝ Mn ⎝ Mn ⎠
The wet brush thicknesses of the swollen PHEMA chains dissolved in a good solvent (water), LXRR (nm), were determined using in situ XRR analysis at room temperature. For PHEMA brushes on the SR, grafting parameters for PHEMA brush were calculated from dry thicknesses obtained by XRR measurements using eqs 2.2−2.4. Indicative values of grafting parameters as well as Flory radii RF of PHEMA brush obtained by surface-initiated ATRP for different polymerization times and also initiation efficiencies Σ/σ are reported in Table 2. Depending on polymerization time, results indicated a grafting density between 0.59 and 0.61 (chains/nm2) and grafting distances ranging from 1.44 to 1.47 nm. The impact of the initiator surface density on the surface initiated ATRP of PHEMA is further illustrated when comparing the initiation efficiencies (Σ/σ) with respect to the PHEMA graft densities (Σ) in Table 2. The comparison shows that starting from a surface covered with BrTMOS initiator allows the formation of a polymer brush with extremely high graft densities and higher initiation effeciency. Most interestingly, comparisons of average distances between grafting sites s with twice the value of Flory radius, representing
(2.4)
ρp is the density of dry grafted polymer films. The density of the PHEMA and diblock PHEMA-b-PNIPAM brushes was determined by the fit of the X-ray reflectivity. For the PHEMA brush the value was 1.1 g/cm3 equal to the literature value89 of an unbounded chain. For the PHEMA-b-PNIPAM diblock copolymer brush case the value was 1.21 g/cm3, slightly above the literature values of PHEMA and PNIPAM.90 For the error of film thickness ΔH = 1 nm was chosen, which is the error of XRR modeling. The error of the molecular weight ΔMn was set to 4% of the measured molecular weight. To determine whether the grafted polymers are in the brush regime, we calculated the distance between grafting sites s relative to the Flory radius RF = an3/5,91 assuming that water is a good solvent for PHEMA. Here, a is the effective segment length (assumed to be ∼3.78 Å for HEMA monomer92,93 and ∼3 Å for NIPAM monomer94) and n is the degree of polymerization. If s ≪ 2RF, then the chains form stretched brushes. 5264
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Table 3. Summary of PNIPAM Second Block Grafting Parameters polymerization time (h)
H (nm)
Mn/1000
PDI
Σ (chains/nm2)
ΔΣ (chains/nm2)
s (nm)
RF (nm)
s/(2RF)
Rc (nm)
s/(2Rc)
0.5 1 3 4 7 15
9.45 16.32 28.12 35.82 65.34 68.32
11.90 23.38 42.76 52.14 99.85 110
1.25 1.19 1.18 1.18 1.17 1.18
0.55 0.54 0.51 0.53 0.51 0.51
0.06 0.03 0.02 0.02 0.02 0.02
1.52 1.54 1.58 1.55 1.58 1.58
4.9 7.35 10.55 11.9 17.56 18.61
0.15 0.1 0.07 0.06 0.05 0.04
1.41 1.77 2.16 2.32 2.87 2.97
0.52 0.43 0.36 0.33 0.27 0.26
PHEMA and PNIPAM blocks, repectively. Evidently, the PHEMA block brought negligible influence from the temperature change. These consecutive decreases in film thickness indicate clearly that the PNIPAM block undergoes an abrupt structural change from brush-like to a mushroom-like state across the LCST. Further increases in temperature lead to the formation of a brush that displays a rather low overall thickness ∼19.6 nm, and the fitted reflectivity curve also showed the increase in roughness by a factor of ∼3, which is also clearly visible by vanishing of all but one of the Kiessig fringes. Above the LCST temperature, the overall diblock copolymer brush thickness is very close to the height of PHEMA block at dried state and supports the complete collapsing of PNIPAM chains over the PHEMA layer. To further verify the adsorption of the PNIPAM chains on the PHEMA-modified SR surface, GATR-FTIR and XPS were used on a sample with a XRR obtained PNIPAM thickness of ∼10 nm (see Figures S5b and S7, respectively). The recorded kinetic plots and GPC traces of PNIPAM free polymers are depicted in Figure S8. To decide whether the prepared PNIPAM second blocks are brushes, we used the same brush criteria that already applied in the case of PHEMA first block in the previous section. The distance between grafting sites is compared to twice the radius of gyration Rg of a free chain, leading in the case of direct comparison to the brush criterium of s/(2Rg) ≪ 1, but also a comparison to the area πRg2, which a free chain would occupy, is possible and leads to a difference in the calculated reference value of a small factor.2 We used the first brush criterion, which was already applied for PNIPAM brushes, and determined Rg for good and bad solvent conditions given by the polymer solution theory.96,97 For good solvent conditions (e.g., PNIPAM in water below the LCST), the distance between grafting sites s is compared to the Flory radius RF = an3/5, and for bad solvent condition, the radius of a collapsed chain Rc = an1/3 has to be considered in the brush criterion. Since Rc is smaller than RF, the bad solvent conditions are the tighter conditions if the PNIPAM films are in the brush regime. Strictly, the formulas for Rg at different solvent conditions were developed for classical neutral brushes with no specific interaction with the solvent molecules, and deviations exist for PNIPAM brushes from the experimentally determined Rg up to 40%, where Rg is decreased below and slightly increased above the LCST compared to the classical theory.98 With respect to these results, the use of the persistence length rather than the monomer size to calculate Rg should be discussed. Additionally, there can be found slightly different values for the monomer size a in the literature.99 The calculated grafting data of PNIPAM second block are presented in Table 3 for different NIPAM polymerization times. As can be seen, with respect to the brush criterion, all PNIPAM layers at different grafting times presented in this paper are in the brush regime below the LCST at good solvent
the dimension of unperturbed chain in good solvent, gave in all cases a ratio inferior to 1. As it is generally admitted for grafted polymers, s/2RF < 1 indicates a “brushlike” conformation of the PHEMA chains in good solvents. Also in Table 2, the investigation of the swollen PHEMA brushes thicknesses using in situ XRR measurements in water gave LXRR values much superior to RF, which indicated a fully stretched conformation for PHEMA chains at ambient conditions. C. Sequential Addition for Preparation of Diblock Copolymer Brushes via Surface-Initiated ATRP. The fabrication of PNIPAM block is outlined in Figure 2 and can be successively grown from the PHEMA macroinitiator by the “living” characterization of ATRP. To synthesize PHEMA-bPNIPAM DCBs with various PNIPAM chain lengths, samples from the same PHEMA batch featuring ∼6.65 nm dry height (∼nm wet height obtained by in situ XRR analysis under water environment; Figure 1 and Table 2) were exposed to ATRP polymerization conditions described in the experimental sections. The results of XRR measurements confirm the successful preparation of PNIPAM block. The typical in situ XRR spectra of the PHEMA-b-PNIPAM brushes on the SR substrate under liquid environment (deuterated water) with different solution temperatures are shown in Figure 1. For the reported cases, the first prepared PHEMA block yielded a ∼ 12 nm (wet thickness) thick film with a relative low roughness of Rrms = 0.5 nm (Figure 1b). The following grafting of the second PNIPAM block led to wide-range changes in thickness after exposing to different solution temperatures due to the LCST of the polymer at ∼32 °C. Below LCST, the PNIPAM brushes assume a stretched conformation as a result of intermolecular hydrogen bonding with water, resulting in a hydrophilic behavior.95 However, at LCST, the brushes undergo a phase transition, resulting in a collapsed brush conformation due to intramolecular hydrogen bonding and resulting in reduced wettability of the surface.95 Here, the phase transition of the PNIPAM block is reflected as a change in total diblock height originated from a change in PNIPAM block thickness. These change in structure can also be seen by XRR. Figure 1c,d shows that when analyzed below the LCST temperature, the height of PHEMA-b-PNIPAM diblock copolymer brushes was ∼34.4 nm (stretched state) with a root-mean square roughness of Rrms = 0.5 nm, confirming that the surface was smooth. In order to check the validity of three-layer model, we tried to analyze the whole diblock copolymer brush system using a four-layer model Si/SiOx/initiator/PHEMA/PNIPAM, and the results yielded thicknesses of ∼11.2 nm for PHEMA block and ∼22.8 nm for PNIPAM block. The result shows a nearly perfect agreement with the thickness obtained for homopolymer brush of HEMA grown from the initiator-modified SR surface. When the temperature was increased close to the LCST, 32 °C, the resulting film yielded a thickness of ∼22.3 nm and an increase in roughness to Rrms = 0.6 nm. A further analysis by the fourlayer model also reveals ∼10.8 and ∼11.5 nm thicknesses for 5265
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Figure 3. (a) Thickness of PNIPAM second block of high density PHEMA-b-PNIPAM DCB as a function of temperature in water. The dry state thickness is also shown for the sake of comparison. (b) Static water contact angles under dry conditions and static air bubble contact angles under liquid environment (DI water) underneath high-density PHEMA-b-PNIPAM DCB. Inset plot shows the derivative curve air bubble contact angle (dθ/dT) versus temperature.
conditions. At bad solvent conditions they are no longer in the brush but are presumably in the mushroom regime. Additionally, the transition between brush and mushroom regime is affected by the statistics of grafting and the polydispersity of the brush polymers, leading to a less sharp transition and a larger zone of intermediate grafting densities between these two regimes.2 As can be seen later from Figure 3, the deswelling is not complete, but the brush quality should be considerably reduced above the LCST. Thus, the deswelling process presented in the all in situ measurements can be considerably influenced by a transition from the brush regime to a crossover and to the mushroom regime. D. Thermal Switching of Physicochemical Surface Properties of Thermoresponsive PHEMA-b-PNIPAM DCB in Water. After layer fabrication, it was imperative to test the LCST phase behavior of PNIPAM confined within the DCB structure. It is well-known that PNIPAM to be sensitive to a variety of environmental conditions such as temperature and salt concentration,45,100,101 and our hypothesis here is that this collapse/swelling will change the overall vertical layering of PHEMA-b-PNIPAM DCB, leading to a distinct variation of the physicochemical surface properties and molecular structure of DCB. Homopolymers, hydrogels, and tethered chains of PNIPAM show a LCST around 32 °C.101−103 Below the LCST the polymer adopts a coiled structure, and above this temperature it collapses into a more globular form. In the case of a PNIPAM brush, one should be able to take advantage of its temperature sensitivity to control the thickness of the grafted polymer layer, which could have a number of practical applications. The reversible conformational changes of thermoresponsive PHEMA-b-PNIPAM DCB were investigated in different ways. To monitor this, we first measured the thickness of PNIPAM block (because the swollen PHEMA chains in water showed no significant change in their height with temperature changes in the range of our temperature limit) above and below the LCST with in situ XRR analysis in deuterated water. Figure 3a shows the change in the second PNIPAM block thickness of the high-grafting-density PHEMAb-PNIPAM DCB with dry thickness of 9.45 nm in deuterated water with changing temperature. Initial XRR tests done in air
at different temperatures showed no change in thickness of PNIPAM chains (see Figure 3a). In fact, several recent reports claim that PNIPAM layers respond strongly only if they are also in a favorable solvent (such as water) and that the transition is not apparent under ambient conditions.104,105 Indeed, the same measurements in water revealed significant changes. The PNIPAM layer reached a thickness of around 22.8 nm at 20 °C, and the layer thickness collapsed to 9.46 nm above the LCST (Figure 3a). Just for the sake of comparison, the fully extended chain length (contour length) of the directionally fully stretched PNIPAM second block can be estimated from its molecular weight,106 which for the sample considered in Figure 3a (9.45 nm dry thickness of PNIPAM block) is 11.9 kg/mol and equals about 105 NIPAM monomers. Using the literature reported data (C−C bond length of 1.54 Å and a ∠CCC of 110.5°107), the PNIPAM second block contour length is estimated to be ∼26 nm. Therefore, in a swollen PHEMA-bPNIPAM DCB end-to-end distances are very close to the PNIPAM contour length, indicating that the chains are so highly stretched to be close to fully extended conformation. It can consequently be argued that it is the limit in the stretching of PNIPAM chains which settles the maximum amount of water pickup by the PHEMA-b-PNIPAM DCBs. This rough argument, to be corrected by the entropy loss of highly stretched chains, can be used as a rational to understand the differences in water pickup by different hydrogel structures.108 This thermoresponsive reversible conformational changes of PHEMA-b-PNIPAM DCB was further assessed by the static water contact angles under dry conditions and captive air bubble method in aqueous solution. Generally, the hydrophilicity/hydrophobicity of material surfaces can be determined by placing a sessile drop on the dry surface. We preferred to further examine hydrophilicity by the captive air bubble method as the material changed its interfacial character in response to the type of environment, air or aqueous medium. Indeed, the outer PNIPAM segments at the surface of PHEMA-b-PNIPAM DCB can reorient slowly in a few hours as shown by the contact angle of a sessile drop of water which decreased from about 35° after droplet deposition to less than 5° after 1 h under 80% relative humidity before evaporation of the droplet 5266
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Figure 4. 3D in situ AFM height image under liquid environment (DI water) obtained for the densely grafted PHEMA-b-PNIPAM DCB at (a) 20 °C and (b) 40 °C. (c) High-magnification AFM height image with phase overlay of the boxed region in (b).
at 25 °C (data not shown). The contact angle measurement using a captive air bubble is a versatile and reproducible technique to quantify the extent of hydrophilicity/hydrophobicity of water-attracting polymeric substrates in contact with water. Figure 3b shows temperature dependence of the static water contact angles under dry conditions and static air bubble contact angles in aqueous conditions at the surface of PHEMA-b-PNIPAM DCBs with the grafting density of approximately 0.53 chains/nm2. For each data point, the sample was equilibrated at the measurements temperature for 10 min before measurement of the contact angle. As shown in this figure, the water contact angle curve exhibits a sigmoidal with three well-defined plateau regions at low, medium, and high temperatures and two smooth transitions in between. The data for PHEMA-b-PNIPAM layer on SR surface show no distinctive changes at any point throughout the transition. Therefore, we plotted the first derivative of water contact angle as a function of temperature (data not shown here), which showed the wetting transition temperatures of DCB as 28 and 35 °C. These results are indeed in good accord with the transition temperatures obtained for dry PNIPAM brush on flat silicon wafer.109 The thermoresponsive behavior of PNIPAM brushes from a hydrophilic surface to a partially hydrophobic one is consistent with the LCST behavior of PNIPAM in solution, where intermolecular H-bonding between PNIPAM chains and water becomes intramolecular H-bonding within PNIPAM chains as temperature increases across the LCST and the DCB exhibits a broader range than that of polymers in solution. For highly ordered SAMs, contact angle measurements have been shown to be sensitive to the outermost ∼2 Å, whereas water senses the depth groups down to ∼5 Å beneath the surface.110 The greater sensing depth of water may reflect its penetration through second block PNIPAM chains at the surface of PHEMA-b-PNIPAM layer. The polymer segments in the outermost region of the PNIPAM second block remain highly solvated until the dilute solution LCST (∼32 °C), while densely packed, less solvated segments within the brush layer undergo dehydration and collapse over a broad range of temperatures.37 The double dewetting transitions can be further explained by invoking the n-clusters concept developed by de Gennes et al.111 They suggested that chain segments in the inner region of polymer brushes can exhibit attractive n-body interactions while the two-body interactions are still weakly repulsive, initiating the collapse of chain segments densely packed in the inner region. Kidoaki et al. noted that the collapsed PNIPAM brush surface exhibits low hydrophilicity, which indicates that the
outermost surface of the collapsed PNIPAM layer undergoes weak hydration.112 By dipping the sample in water, the static air bubble contact angle also changes underneath the PHEMA-b-PNIPAM grafted layer as a function of temperature (Figure 3b) through a different trend as compared with the past results reported in the case of PNIPAM homopolymer brush and also with those obtained for water contact angle measurements. Here, θ indicates the mean contact angle of θ’s at several different locations on the respective sample. As shown in Figure 3b, with increasing temperature from 20 to 24 °C, the air bubble contact angle of the PHEMA-b-PNIPAM DCB slightly increases and then decreases at around 30 °C, followed by a rapid decrease at around 32 °C. The dewetting transition temperatures of PHEMA-b-PNIPAM DCB were more observable from the firstderivative curve of the air bubble contact angle (absolute value of dθ/dT) as a function of temperature (see inset to Figure 3b). As shown in this plot, the dewetting transition temperatures were detected as 24 and 32 °C, which are in good agreement with previously reported data for the smooth PNIPAM gels.113 According to the n-clusters concept, the former transition point for high density PHEMA-b-PNIPAM DCBs at lower temperatures may be attributed to the decrease in the hydration ability of the polymer chains even in the vicinity of the surfaces and also the localization of the alkyl bromide end groups of the PNIPAM second block to the surface of the DCB due to the stretched state of the PNIPAM chains. The second transition at 32 °C can be attributed to the LCST of PNIPAM chains that more realized via air bubble contact angle technique due to the highly precise controlled living polymerization that leads to the formation of a smooth homogeneous diblock layer on the SR surface. The temperature-induced change between extended and collapsed states of PHEMA-b-PNIPAM DCB was directly observed using in situ AFM analysis with the sample in liquid environment. Figure 4a shows that when imaged under water at 20 °C (below the LCST), the surface of the DCB was essentially featureless (extended state), and only very subtle indications of any structural features were seen. The surface being essentially flat and the value of Rrms is 0.60 nm over 25 μm2 using the AFM (very close to the roughness value obtained from XRR analysis at below the LCST), which shows that the surface is very smooth. When the temperature was increased up to 40 °C (above the LCST of PNIPAM), one can observe that the morphology of DCB has turned from needle-like to domain-like structure and a large number of nanodomains were seen to appear on the 5267
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image (Figure 4b). This morphology most resembles a “matrixisland”, in which the PNIPAM nanosized islands were distributed over the highly-packed PHEMA layer. This change in structure is accompanied by a large increase in roughness from Rrms = 0.60 nm to Rrms = 1.50 nm over 25 μm2. Multiple line cuts were performed on a locally magnified picture of Figure 4b over 0.25 μm2 to measure the distance between nanodomains. The boxed area in Figure 4b was scanned by AFM, and the obtained image is depicted in Figure 4c. The analysis resulted in an average center-to-center distance of 25 ± 5.5 nm of the nanodomains. These images indicate clearly that the PNIPAM second block within the PHEMA-b-PNIPAM layer undergoes an abrupt structural change from a brush-like to a mushroom-like state across the LCST. The change in the structure was already illustrated by XRR (Figure 1), in which the fitted reflectivity curve also confirmed the increase in roughness by a factor ∼3, which also clearly visible by vanishing of all but one of the Kiessig fringes. Finally, the reversible conformational change of PHEMA-bPNIPAM DCB as a result of thermoresponsive nature of second PNIPAM block was examined by grazing incidence small-angle X-ray scattering to obtain a more averaged and quantified information on the films morphology. To prove the uniformity of the PHEMA-b-PNIPAM DCB over larger lateral length scales and to investigate the lateral structure of the PNIPAM second block below and above the LCST temperature within the DCB, μGISAXS measurements were performed. μGISAXS scattering patterns yield averaged structural information on the illuminated sample spots. The incident angle was set to αi = 0.4°, which is above the critical angles of both the polymer blocks and the SR substrate.114 Outof-plane cuts, at an exit angle equal to the critical angle of PNIPAM, αc = 0.148°, were performed (Figure 5), enabling us to obtain averaged structure information about the domain-like PNIPAM structures above the LCST in the range of several nanometers to ∼350 nm. For a closer data analysis, the out-of-plane cuts presented in Figure 5 were fitted according to the unified fit model to reveal structural features on multiple levels. It combines Guinier exponential and structurally limited power-law regimes. The horizontal GISAXS data of PHEMA-b-PNIPAM DCB obtained at 40 °C (after treatment of DCB under deuterated water at 40 °C for 1 h) transverse scattering from two structural levels, which are separated by a correlation broad interference peak, can be observed. The found Porod decay of ∼2.8 at high q (solid green line) suggests the presence of PNIPAM islands with an Rg = 8.9 ± 1.5 nm and a mean center-to-center correlation length of ξ = 22 ± 5 nm. Accordingly, a fit discrepancy toward AFM results of 10% can be assigned, which is even better than the error estimated by simulation. Therefore, the average PNIPAM island distance with the corresponding standard deviation is in very good agreement with the average distance value of the repetition period of the domain structure observed from the AFM images. The 2D GISAXS pattern for the PHEMA-b-PNIPAM DCB at 40 °C, shown in the right inset to Figure 5, contains remarkable scattering peaks to the left and right of the plane of incidence, which intersects the detector at the center of the image. Because of the resolution restriction in our experimental qy range, we were only able to record a few data points, which account for Porod scattering of level 2. However, the found power-law decay of P ≈ 1.5 at low q (dashed green line) can give evidence to a mass fractal, which may be related to
Figure 5. Double-logarithmic μ-GISAXS plots of the out-of-plane cuts of the PHEMA-b-PNIPAM DCB as a function of the qy component of the scattering vector at 20 °C (bottom) and 40 °C (top). The dashed line represents the resolution limit of the μ-GISAXS experiment. Colored lines are the fits, from unified fit model, for determining the prominent in-plane length scales, corresponding to the scattering data in black below them. The upper curve is shifted along the vertical axis for improved visualization. The inset pictures show the 2D scattering pattern at 20 °C (left) and 40 °C (right).
subnanodomains with low anisotropy. As visible from the wide peak in the GISAXS scan, the domains have a broad size distribution. A single domain consists of roughly 50−120 single polymer chains. The broad size distribution is probably related to the formation of subnanodomains with low anisotropy. These subnanodomains can be originated from the fact that the thermally induced collapsed state of the outermost surface of the PNIPAM second block within the PHEMA-b-PNIPAM DCB is very different from that for the whole film. It may be that the polymer segments in the outermost region of the brush have weak interchain interactions, while densely packed segments within the brush layer have strong and intra- and interchain interactions and collapsing over a broad range of temperatures leads to the formation of subnanodomains in the collapse state. The error in the center-to-center distance extracted from the line cuts of the AFM images is another evidence of this. The fitted power-law exponent of P ≈ 2.8 is also another evidence of a domain-like morphology, proposing an arrangement of PNIPAM islands in a arbitrary threedimensional mass fractal.115 Decreasing the temperature below the LCST leads to disappearance of nanodomains from the DCB surface and to formation of needle-like structure of DCB, indicating the highly stretching state of DCB chains on the SR surface. It results also in the contrast necessary for detection of the in-plane length scale from nanodomains with GISAXS. The corresponding 2D GISAXS pattern was also showed in the left inset to Figure 5, indicating no remarkable scattering features to the left or right of the center. This indicates that the structure of the PHEMA-b-PNIPAM DCB is uniform along the y direction in the plane of the sample, even though it has a highly asymmetric composition. E. Trace of the Thermally Induced Reversible Conformational Change of PHEMA-b-PNIPAM DCB Using in Situ FTIR Measurements. In the present section, we present our in situ FTIR study of the chain collapse and 5268
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Figure 6. Temperature-dependent in situ FTIR spectra of the PNIPAM top block within a high-density PHEMA-b-PNIPAM DCB in D2O (20−40 °C) during heating−cooling cycle with an interval of 0.5 °C: (a) ν(CH) upon cooling; (b) ν(CH) upon heating; (c) ν(CO) upon cooling; (d) ν(CO) upon heating. Insets: determination of the isosbestic point of ν(CH) overlaid spectra during cooling (left panel) and heating (right panel). Three curves at 20, 33, and 40 °C are highlighted for good observance.
PHEMA bottom block in D2O solution during cooling and heating processes, respectively. As reported, the transition temperature of the polymer gel in D2O is 0.7 °C higher than that in H2O. However, the deuterium isotope effect does not cause obvious changes on the magnitude of hysteresis.117,118 Examining carefully the spectral variation of two investigated regions in Figure 6 (C−H stretching bands in 3030−2830 cm−1 and CO stretching band in 1675−1580 cm−1), we can find that the both wavenumbers and areas of C−H and CO groups obviously change during heating and cooling processes. The detailed absorption bands centered at about 2981, 2938, 1649, and 1624 cm−1 can be attributed to the vibration of νas(CH3) of the side chains of PNIPAM,116,119 νas(CH2) of the main chains,116,119 amide I (CO hydrogen bonded with N− D, in accordance with the equation PNIPAM + D2O ⇋ −ND + HDO),116,120,121 and amide I (CO hydrogen bonded with D−O−D),116,120,121 respectively. The C−H stretching bands shifted slightly to higher frequency (hydrated state) upon cooling, while an inverse shift occurs for a heating process. The intensity of the amide I group at 1624 cm−1 remains constant from 20 °C up to ∼32 °C, but above that, it decreases while the intensity of the 1649 cm−1 band increases (for clarity, not all the spectra are shown in Figure 6c,d). One can immediately see
revival thermodynamics of PHEMA-b-PNIPAM DCB during heating and cooling processes to get an insight into the molecular motion and interaction between groups, mainly by the two-dimensional correlation spectroscopy (2Dcos) technique. IR spectroscopy is rather sensitive technique to morphology and conformational changes by reflecting subtle information at the molecular level. Results from XRR and contact angle measurements provided an appropriate temperature range to perform in situ FTIR experiment and give precise information about the LCST and extent of phase transition revival of PHEMA-b-PNIPAM DCB. D2O, rather than H2O, was used here as the solvent to eliminate the overlap of the bending vibration band of H2O (δ(O−H)) observed around 1640 cm−1 with the amide I band (ν(CO)) of PNIPAM (whereas that of D2O appears around 1200 cm−1), as well as the broad ν(O−H) band of H2O around 3300 cm−1 with the ν(C−H) bands of PNIPAM second block.116 To understand the chain stretching and chain collapsing of PHEMA-b-PNIPAM DCB during phase transition, a series of conventional FTIR spectra have been collected at the interval of 0.5 °C between 20 and 40 °C. Figures 6 and 8 show the temperature dependence of the absorption bands of the C−H and CO groups of PNIPAM top block and CO group of 5269
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Figure 7. Baseline-subtracted amide I bands measured during the heating and cooling process. The color lines indicate the Gaussian fit to identify different components.
water molecules through networks. On the other hand, the presence of isosbestic points in the cooling process indicates that the chain revival of PNIPAM layer occurred with only conversion between two single states, which may arise from local phase transition due to the less free diffusion of water molecules. For further clarification of this issue and to investigate the molecular situation of the PNIPAM second block within a highdensity PHEMA-b-PNIPAM DCB, the ν(CO) band is fitted with Gaussian curves according to the results obtained from the heating/cooling experiments, as presented in Figure 7. Here, spectra at four different temperatures during the heating and cooling process are chosen as examples. Curve fitting reveals that two bands are necessary to match the spectra at different temperatures satisfactorily. In Figure 7, as the temperature increased from 20 to 40 °C, the amide I band of PNIPAM second block (black curve) exhibited a sigmoidal shift during phase transition. One can immediately see that the two components of the deconvoluted amide I band were centered at 1624 and 1649 cm−1 at any temperature. The intensity of the peak at 1624 cm−1 decreased with temperature, while that at 1649 cm−1 increased. The band at 1624 cm−1 exist at lower frequency contributed from doubly H-bonded carbonyl groups with water molecules below LCST of PNIPAM second block. As temperature increases, the band at 1649 cm−1 appears and increases gradually, which is evidence of another form of CO groups. As shown in Figure 7, the band at 1649 cm−1 can usually be assigned to the CO···D−N hydrogen bonds in a nongrafted PNIPAM aqueous solution containing amide groups and water molecules.120,125 So, the results can be described as that the hydrogen bonds from different amide groups begin to form above the LCST upon temperature increases and the PNIPAM chains within the PHEMA-b-PNIPAM DCB exhibit a coil−globule-like transition similar to the transition shown by linear PNIPAM in a aqueous solution.
that the CO exhibits a binary spectral intensity change, in which the peak shape of the CO groups undergoes a strange transition from a asymmetrical form (a single Gaussian component centered at 1624 cm−1) to a relatively symmetrical form during cooling. During heating the case is just opposite to that in the cooling process. Evidently, in the PNIPAM system, the CO interacts predominantly with D2O at the initial heating and leads to the formation of a relatively symmetrical spectra. After temperature increasing, only a portion of C O···D2O have been consumed and changed to another kind of hydrogen bond (CO···DN).122 Therefore, the CO···D2O and CO···DN are inclined to coexist in the PNIPAM system, leading to the asymmetrical peak shape of CO groups. The chain revival process during cooling had the inverse changes. It was shown, as previously reported for PNIPAM linear polymer in a solution state, an isosbestic point can be observed at 1637 cm−1 during the change in temperature across the LCST of PNIPAM.116,123,124 Isosbestic behavior means that two distinct absorption species exist and that the components of the IR bands due to the species are constant in position and band shape and change only in intensity. In order to determine whether there existed isosbestic points in νas(CH3) overlaid spectra during heating and cooling in PHEMA-b-PNIPAM DCB, two enlarged spectra with three highlighted curves at 20, 33, and 40 °C are displayed as inset pictures in Figure 6a,b. Interestingly, only the cooling process exhibits an isosbestic point at about 2980 cm−1, while the heating process has no strict isosbestic point. We also observed another isosbestic point in ν(CO) overlaid spectra only in cooling process at 1638 cm−1 during the superimposition of the absorption spectra of the amide I band (Figure 6c). Maeda et al.116,121 already observed a similar phenomenon in the case of PNIPAM hydrogels and believed that the absence of isosbestic points in the heating process indicates that the chain collapse of PNIPAM occurred with some intermediate states or a completely continuous phase transition, which may result from a holistic phase transition due to the free diffusion of 5270
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Figure 8. Temperature-dependent in situ FTIR spectra of the PHEMA bottom block within a high-density PHEMA-b-PNIPAM DCB in D2O (20− 40 °C) during heating−cooling cycle with an interval of 0.5 °C: (a) 3D spectra of the ν(CO) during heating; (b) 2D spectra of the ν(CO) during heating; (c) 3D spectra of the ν(CO) during cooling; (d) 2D spectra of the ν(CO) during cooling.
that during heating ν(CO) bands mainly change in two aspects: (1) the band initially located at 1728 cm−1 gradually blue-shifts to a higher wavenumber; (2) in addition to the position change, the area of ν(CO) bands increases at the beginning from 20 °C to about 34 °C but maintains constant in the following heating process. In Figure 8c,d, when the temperature drops, there is an almost constant position concerning the band of ν(CO) with a constant intensity from 40 °C to about 34 °C followed by an intensity decrease below 34 °C at about 1728 cm−1, which is opposite to the changes upon heating. The reasons for this strange behavior observed for molecular movement of bottom block PHEMA chains within a high density PHEMA-b-PNIPAM DCB grown from a SR surface are not fully understood at the moment and are the subject of ongoing investigations. It may well be, however, attributed to the fact that although high molecular weight HEMA homopolymer is hydrophilic and has a relatively high degree of hydration (up to 42% water can be absorbed per unit mass of lightly cross-linked PHEMA based gels126), it is generally regarded as being only water-swellable, rather than watersoluble.127−129 However, this observation may well be related
It should be pointed out that the area experiences an obvious variation upon cycling up and down in temperature. If we assume a 1:1 conversion of the CO species, integrated areas of amide I band of a high-density PHEMA-b-PNIPAM DCB (that are equal to absorbance in a sense, and the absorbance can be described according to the Beer−Lambert law: Ii = aibc, where ai is the absorption coefficient, b is the path length, and c represents the concentration of the species) measured at various temperatures give the ratio of the molar absorptivity of 1624 cm−1 band relative to that of component at 1649 cm−1 band as ∼0.60 at 40 °C. This molar fraction was accounted for about 0.85 of the total area of the spectrum at ∼20 °C. This means that the PNIPAM chains shows slightly a collapsed state even at a sufficiently low temperatures below the LCST. As above, the PNIPAM chains within a high-density PHEMA-bPNIPAM DCB are in spatially constrained state and cannot fully interact with water molecules. Figure 8 shows the temperature dependence of the absorption band of the carbonyl stretching vibration of the ester group (ν(CO)) of PHEMA bottom block at 1728 cm−1 during a single heating and cooling cycle between 20 and 40 °C under D2O environment. In Figure 8a,b, we can clearly observe 5271
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Figure 9. (a) Synchronous and (b) asynchronous maps of the ν(CH) and ν(CO) regions during the heating process of the PNIPAM top block within a high-density PHEMA-b-PNIPAM DCB. (c) Synchronous and (d) asynchronous maps of the same regions during the cooling experiment. The warm colors (red, yellow, and green) are defined as positive intensities while cold colors (blue and cyan) as negative intensities.
ν(CO) bands during heating reveal that the molecular behavior of PHEMA chains is accompanied by the dehydration of hydrophobic C−H groups, the disassociation of C O···D2O hydrogen bonds, and formation of low-diluted PHEMA chians. The chain revival process during cooling had the inverse changes. Figure 8a represents that the band initially located at 1728 cm−1 at room temperature gradually blue-shifts during heating and eventually arrives at 1732 cm−1 at about 34 °C. On the basis of previous research,131−133 we know that peaks of CO···H2O with various strengths locate at different positions; the stronger the CO···H2O is, the lower its wavenumber is. Therefore, the blue-shift of the ν(CO) peak indicates the weakening of CO···H2O during heating. Judging from primitive in situ FTIR analysis of bottom block PHEMA chains within a high-density PHEMA-b-PNIPAM DCB, PHEMA bottom block has a large similarity to watersoluble HEMA homopolymer,130 indicating that our “pseudo soluble−insoluble” phase transition hypothesis of grafted highdensity PHEMA chains is closely probable. F. Two-Dimensional Correlation (2Dcos) Analysis. Based on the above analysis and results, the different features of phase transition in the solution of a high-density PHEMA-bPNIPAM DCB and D2O have been discussed. To extract
to the presence of low levels of ethylene glycol dimethacrylate often found in HEMA monomer, which could lead to an extrinsic cross-linking reaction during its homopolymerization. Indeed, above a target degree of polymerization of 40, waterinsoluble fractions were observed, as expected. Moreover, Weaver et al. showed that lightly cross-linked HEMA homopolymers with mean degree of polymerizations between 30 and 45 and polydispersities between 1.2 and 1.1 synthesized by the ATRP technique exhibited inverse temperature solubility (cloud point) behavior in dilute aqueous solution ranged from 28 to 40 °C.130 They confirmed a linear relationship between the molecular wights and the respective cloud points. Although our inspected molecular weights regarding the PHEMA bottom block are higher than the solubility range of HEMA homopolymers, absence of cross-linker traces (as shown by SEC) and in-range polydispersity values allowed for suspected interpretation. On the other hand, a closer inspection of the apparently water-insoluble higher-molecular-weight HEMA homopolymers revealed that a significant proportion of these samples was dissolved between 20 and 30 °C.130 Therefore, the changes of ν(CO) bands of PHEMA bottom block can be roughly explained by a “pseudo soluble−insoluble” interaction of polymer with neighboring water molecules. The changes of 5272
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Figure 10. (a) Synchronous and (b) asynchronous maps of the ν(CO) regions during the heating process of the PHEMA bottom block within a high-density PHEMA-b-PNIPAM DCB. (c) Synchronous and (d) asynchronous maps of the same region during the cooling experiment. The warm colors (red, yellow, and green) are defined as positive intensities while cold colors (blue and cyan) as negative intensities.
tively. 2D synchronous spectra provide information about simultaneous changes between two wavenumbers. The red, yellow, and green colored and blue and cyan colored regions in 2Dcos contour maps represent positive and negative crosspeaks, respectively, throughout this paper. 1. PNIPAM Top Block: Heating Process. The synchronous and asynchronous maps for the heating process of the PHEMAb-PNIPAM DCB in D2O solution are shown in Figures 9a and 9b for the 1680−1570 and 3025−2900 cm−1 regions corresponding of CO stretching and C−H stretching bands of PNIPAM top block. For the CO region, the synchronous spectrum (Figure 9a) is dominated by two strong autopeaks at 1649 and 1624 cm−1 and a negative cross-peak at (1649, 1624) cm−1. The above two autopeaks are attributed to the vibrations of the CO···D−N and CO···D−O−D hydrogen bonds, respectively.116,120,121 As it is negative in the synchronous contour plot, the cross-peak of (1649, 1624) cm−1 helps to infer that the two species of carbonyl hydrogen bonds transform in opposite directions (one increase, while the other one decreases). On the other hand, with the positive cross-peak at (1649, 1624) cm−1 in the asynchronous map of Figure 9b, Noda’s rule can help to conclude that the peak of 1624 cm−1 alters before that of 1649 cm−1 when temperature rises, which
additional useful information about conformational changes, we employ 2Dcos analysis to more explore the microdynamics mechanism of the phase transitions. In 2Dcos analysis, two types of correlation maps (synchronous, Φ, and asynchronous spectra, Ψ) are obtained from a series of dynamic spectra, which are both characterized by two independent wavenumber axes (ν1, ν2) and a correlation intensity axis. Synchronous spectra are symmetric with respect to the diagonal line in the correlation map, while the asynchronous spectra are asymmetric with respect to the diagonal line in the correlation map. Furthermore, with crosspeaks appearing in both synchronous and asynchronous maps, we can figure out the change orders of different peaks while the sample is subjected to an external perturbation. According to the Noda’s rules,62−64 if Φ(ν1, ν2) > 0, Ψ(ν1, ν2) > 0 or Φ(ν1, ν2) < 0, Ψ(ν1, ν2) < 0, band ν1 will change prior to band ν2. If Φ(ν1, ν2) > 0, Ψ(ν1, ν2) < 0 or Φ(ν1, ν2) < 0, Ψ(ν1, ν2) > 0, band ν1 will change after ν2. All the FTIR spectra between 20 and 40 °C with an increment of 0.5 °C are applied to generate the 2Dcos spectra. Figures 9 and 10 present the 2Dcos synchronous and asynchronous spectra of PNIPAM top block and PHEMA bottom block during heating and cooling processes, respec5273
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(Figure 9c). As already known above, the peak at 1649 cm−1 is attributed to the vibrations of the CO···D−N hydrogen bonds, and the peak at 1624 cm−1 is attributed to the C O···D−O−D hydrogen bonds.116,120,121 As a negative peak in the synchronous map, the cross-peak of (1649, 1624) cm−1 helps to infer that two species of carbonyl hydrogen bonds transform in opposite directions during cooling, which is the same condition observed in heating process. In the synchronous map of Figure 9d, this cross-peak of (1649, 1624) cm−1 is observed to be negative, as contrasted with heating process. According to Noda’s rule, it can be inferred that the peak of 1649 cm−1 alters before that of 1624 cm−1 during cooling, which means the change of the hydrogen bonding of CO···D−N is prior to that of CO···D−O−D. The hydrogen bonds of CO···D−N will first be destroyed, releasing the carbonyl groups, and the CO groups will further form new hydrogen bonds with heavy water. Figure 9c,d also represents the 2Dcos maps in the 3025− 2900 cm−1 region gained in the cooling process. The autopeaks develop at 2975 and 2933 cm−1 in the synchronous map, pointing out great changes of both peaks with temperature dropping. Similarly, the sequence of group motions of PNIPAM second block within a high density PHEMA-bPNIPAM DCB in the cooling process can also be deduced as follows: 2975 > 2933 > 2985 cm−1, that is, νas(dehydrated CH3) > νas(dehydrated CH2) > νs(hydrated CH3). It can be concluded that, during cooling, the CH3 groups surrounded with fewer water molecules first hydrate, then some physically entangled chains will disentangle, and finally the CH3 groups will further hydrate with more heavy water. Thus, we can conclude that PNIPAM top block had water molecules diffusing into the network first before the chain revival along the backbone occurred. If we consider only stretching modes, the case is opposite to the heating process. Combining C−H and CO related stretching vibrations (Figure 9c,d), one may see the presence of the cross-peak at (1624, 2975) cm−1 with a same negative symbol in both the synchronous and asynchronous maps, indicating a sequence order as 1624 > 2975 cm−1. Based on the above 2Dcos analysis for cooling process, the sequence order obtained for the C−H region and amide I is 2975 > 2933 > 2985 cm−1 and 1649 > 1624 cm−1, respectively. With the order obtained for the combined spectra, one can immediately extract the transition sequence of all the peaks as follows: 1649 > 1624 > 2975 > 2933 > 2988 cm−1. This suggests that the driving force for chain revival of PNIPAM chains as a top block within a highdensity PHEMA-b-PNIPAM DCB during cooling was the diffusion of water into collapsed brushes. As a conclusion for the cooling process, the whole transition sequences of all bands can be linked as 1649 > 1624 > 2975 > 2933 > 2988 cm−1. Carefully considering the sequence from the 2Dcos analysis, one can discern that the during the cooling process hydrogen bonds of CO···D−N dissociate followed by formation of CO···D2O and include water to polymer, preparing for hydration of CH groups and further promoting the strengthening of CO···D2O hydrogen bonds, H-bonds. After that, H-bonded CO···D2O are strengthened upon the closely full breakage of CO···D−N hydrogen bonds. 3. PHEMA Bottom Block: Heating Process. 2D synchronous and asynchronous maps in the ν(CO) region of PHEMA bottom block during heating from 20 to 40 °C are depicted in Figure 10a,b. As shown above, changes in this temperature region mainly relate to the “pseudo soluble−insoluble” (cloud-
means that the change of the CO···D−O−D is prior to the CO···D−N hydrogen bonding. The carbonyl will first run out of the hydrogen bonds of CO···D−O−D and then will further form the new CO···D−N hydrogen bonding with the D−N group. Furthermore, in the synchronous map of 3025−2900 cm−1 region (Figure 9a), two strong autopeaks develop at 2975 and 2933 cm−1, which point out the prominent changes of these two peaks with temperature elevation. The positive cross-peak at (2975, 2933) cm−1 points that the heating-induced intensity variations of the above two peaks are taking place in a cocurrent direction. Furthermore, the positive cross-peak also implies that out-of-phase spectral changes occur at the two wavenumbers.62 The asynchronous 2D correlation spectrum, shown in Figure 9b, is asymmetric with respect to the diagonal line. As explained by the rule put forward by Noda, the symbols of the cross-peak at (2975, 2933) cm−1 are both positive in the synchronous and asynchronous maps, which infers that when heated, the intensity of the 2975 cm−1 band varies prior to that of the 2933 cm−1 band. In the synchronous and asynchronous maps (Figure 9a,b), the correlation of the 1680−1570 cm−1 region with the 3025− 2900 cm−1 region provides a macroscopic view of the whole phase transition process of PNIPAM second block. The crosspeak at (1624, 2933) cm−1 can be observed in both 2D maps, and the symbol of this peak is negative in the synchronous and positive in the asynchronous maps; thus, we can infer the change order 2933 > 1624 cm−1 in heating. The sequence gained above in the 2D analysis of the CH region and the amide I is 2985 > 2975 > 2933 cm−1 and 1624 > 1649 cm−1, respectively. Therefore, with the order obtained from the correlation of amide I region with respect to the C−H region, one may conclude the transition sequence of all the peaks as 2985 > 2975 > 2933 > 1624 > 1649 cm−1. Other cross-peaks in Figure 9 also validate this whole order of the changes of peaks. These results are in good agreement with the spectra density method analysis of Tamai et al., where the spectral density is obtained from the Fourier transform of the translational velocity autocorrelation function, and it can help to obtain the information about the local motion of water molecules in the solution. They have inferred both the formation and destruction of the hydrogen bonds between N−H and water take place on a very short time scale, faster than the C O···H−O−H hydrogen bonds.134 To summarize, the whole transition sequences of all bands can be linked as 1624 > 1649 > 2980 > 2975 > 2933 cm−1 according to the values in the synchronous and asynchronous maps. In other words, the dehydration order of different groups is dehydrated CO···D−O−D > CO···D−N > dehydrated CH3 > dehydrated CH2. Therefore, the mechanism of phase transition can be concluded as follows: as temperature rises, a large portion of CO···D−O−D changes into the weak hydrogen bonds of CO···D−O−D···OC first, and immediately the strong hydrogen bond of CO···D−N forms. Second, CH3 groups finish their dehydration process before CH2 groups. 2. PNIPAM Top Block: Cooling Process. Herein, 2Dcos is also used to analyze the microdynamic phase transition of the PHEMA-b-PNIPAM/D2O DCB during cooling process. The synchronous and asynchronous spectra of C−H and CO regions are shown in Figures 9c and 9d, respectively. For the CO region, the same negative cross-peak at (1649, 1624) cm−1 can be observed in the synchronous 2D spectrum 5274
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Figure 11. Schematic representation of the proposed structural reorganization of the overall high-density ultrathin PHEMA-b-PNIPAM DCB film in water upon exposure to temperature cycling up and down. Upon cycling down in temperature the PNIPAM chains are highly swollen below the LCST and PHEMA chains are experienced a “pseudo insoluble−soluble” phenomenon and are more hydrated. Whereas, upon cycling up in temperature, PNIPAM is collapsed into tight clusters toward the highly packed and less hydrated PHEMA bottom layer and gets nanophase separated into a structured “matrix-island” topography.
point) behavior of PHEMA chains at 20−33 °C, indicating transformation of strong CO···D2O’s to weaker C O···D2O’s; thus, most correlation peaks in 2D maps would reflect vibrations of various CO-involved hydrogen bonds. The synchronous map shows only an autopeak at 1729 cm−1, which can be assigned to the νas(CO) in CO···D2O. Therefore, its appearance here indicates the CO···D2O structure continues to dissociate during heating within 20−33 °C. There is a negative cross-peak at (1745, 1720) cm−1 in the asynchronous map (Figure 10b). According to its positive symbol in the slice synchronous map (not shown here), we can infer 1720 > 1745 cm−1; namely, 1720 cm−1 should be assigned to a structure that release free water directly. Because 1720 cm−1 has a relatively low wavenumber, this peak is supposed to represent strong hydrogen bonds. Consequently, on the basis of the analysis of this heating region, we understand that hydrogen bonds between heavy water and carbonyl-involved ester group in the PHEMA bottom block are greatly destroyed between 20 and 33 °C. Meanwhile, according to the significant increase of the ν(CO) area, a large number of free water molecules are expelled out of PHEMA matrix in this heating region. 4. PHEMA Bottom Block: Cooling Process. 2D maps, synchronous and asynchronous, in the ν(CO) region of PHEMA bottom block within a high-density PHEMA-bPNIPAM DCB in D2O during cooling from 40 to 20 °C are depicted in Figure 10c,d. Similar to the condition in the heating process, the main changes in this temperature region relate to the “pseudo soluble−insoluble” behavior of PHEMA chains within 33−20 °C. The synchronous map still shows only an autopeak at 1729 cm−1 with the same changing direction under perturbation. Nevertheless, there is no clear cross-peak in the asynchronous map of Figure 10d. According to our experience, such a shape of the asynchronous map is most probable due to the transformation of the intermolecular H-bonding between PHEMA chains and water to the intramolecular H-bonding within PHEMA chains as temperature decreases across the cloud point, and the corresponding asynchronous map does not exhibit any such auto- or cross-peaks over the same wavenumber range. Moreover, according to the cooling-induced changes of the v(CO) peak area in Figure 8c,d, we remember that the area does not increase during cooling at 40−34 °C, and we consider this phenomenon to be caused by incomplete associations of CO···DOD···OC hydrogen bonds so that only limited new interactions might be formed. Here, conclusions of the 2D maps in the cooling process confirm our previous deductions completely.
III. CONCLUSIONS For high analytical efficiency and throughput of SR-based microfluidic, robust and effective surface coatings are necessary for preventing the adsorption of biomolecules on the microchannel surface. In this contribution, high grafting density, ultrathin, thermoresponsive PHEMA-b-PNIPAM DCBs with tunable wettability were successfully prepared under carefully controlled conditions on the surface of SR by the SI-ATRP technique. The surface composition of both SAMBr modified SR substrates and DCBs was monitored by XPS and GATR-FTIR spectroscopy. The tunable wettability and reversible switching between hydrophobicity and hydrophilicity as well as the gradual decreases in the thickness of the densely grafted ultrathin DCBs with temperature were assessed through some in situ analysis of the DCB layers in a liquid environment, which included XRR, AFM, and static air bubble contact angle measurements. At elevated temperatures above the LCST of the PNIPAM top block, the AFM images revealed a lateral microphase separation inside the DCB resulted in the formation of different PNIPAM nanodomains. The morphology of DCB has turned from needle-like to domain-like structure. This morphology most resembled a “matrix-island”, in which the PHEMA layer is covered by PNIPAM domains after collapsing of PNIPAM chains above the LCST (Figure 11). The thermally induced reversible conformational changes of as-deposited, high-density, ultrathin PHEMA-b-PNIPAM DCBs and their respective internal structures were more quantitatively captured using μ-GISAXS experiments before and after switching. The pictured approach, which models scattering in terms of structural levels, can explain structural features via modeling of the transverse detector scans in the qy reciprocal scattering planes. Fitting of the data resulted in domains with an Rg = 8.9 ± 1.5 nm and a center-to-center distance between nanodomains of 22 ± 5 nm. Comparing experimental GISAXS results with particle analysis from AFM studies, we were able to verify mean particle island sizes and center-to-center correlation lengths. In addition, further considerations on domain arrangements, described by packing densities and mass-fractal dimensions, were shown to be useful. Finally, we carried out a detailed study on the molecular mechanism of thermal-induced reversible volume phase transition of high-density, ultrathin PHEMA-b-PNIPAM DCB using an in situ tracing method by FTIR measurements in D2O as the solvent. A newly developed 2Dcos was employed to elucidate the chain collapse and revival behavior of both PHEMA and PNIPAM blocks within a high-density PHEMA-bPNIPAM DCB. 5275
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The Gaussian fitting was adopted to separate different components of the overlaid spectra. The 1649 and 1624 cm−1 were assigned to H-bonded CO···D−N and singly H-bonded carbonyl group with water molecules, respectively. The difference of absorption coefficient of the two components resulted in a decrease of the total area of the amide I region. Quantitative analysis of the C−H region provided that CH3 groups in the outer position of the globular-like polymer had a higher degree of freedom than CH2 groups. We additionally determined the existence of isosbestic points for vas(CH3) and v(CO) overlaid spectra 2970 and 1638 cm−1, respectively, and found, same as PNIPAM hydrogel, that in the heating process the chain collapse occurred with some intermediate states or a completely continuous phase transition while in the cooling process the chain revival occurred with only transition between two single states. The results are consistent with 2Dcos analysis. Detailed spectral analysis of the carbonyl stretching vibration of the ester group of PHEMA bottom block at 1728 cm−1 revealed a “pseudo soluble−insoluble” phase transition behavior, characteristic of the lightly cross-linked PHEMA microgels, at around 33 °C. 2Dcos discerned all the sequence of group motions of both PHEMA and PNIPAM blocks within a high-density PHEMA-b-PNIPAM DCB during cycling up and down.
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ASSOCIATED CONTENT
S Supporting Information *
Experimental section, including materials, synthesis of BrTMOS initiator, experimental procedures, and characterizations; results for (1) water contact angle as a function of UVO treatment time and images showing water contact angles at different treatment times; (2) AFM image of SR surface before UVO treatment and AFM measurements of the SR surface roughness; (3) 1H NMR spectrum for PHEMA and PNIPAM polymers cleaved from the SR surfaces and collected as free polymers, respectively; (4) XPS, GATR-FTIR, and AFM analyses of initiator SAM-Br, PHEMA first block, and PNIPAM second block; (5) all kinetic explanations and plots as well as GPC traces pertain to both blocks. This material is available free of charge via the Internet at http://pubs.acs.org.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected] (F.A.). Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS K. Jalili and A. Milchev are indebted to the Max-Planck Institute for Polymer Research in Mainz, Germany, for hospitality and support during their work on the problem. K. Jalili and F. Abbasi are indebted to Dr. Shigeaki Morita for the software 2D Shige. This research has been partially supported by the Iran National Science Foundation under Project No. 88002464.
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REFERENCES
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