Entanglement of Polymer Chains in Ultrathin Films - American

Nov 2, 2005 - in an ultrathin film do experience entanglement, as has been hypothesized. Thus, we ... decrease in the level of polymer chain entanglem...
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Langmuir 2006, 22, 742-748

Entanglement of Polymer Chains in Ultrathin Films Hideyuki Itagaki,*,†,‡ Yoshiharu Nishimura,‡ and Emiko Sagisaka‡ Department of Chemistry, Graduate School of Electronic Science and Technology, and Department of Chemistry, School of Education, Shizuoka UniVersity, 836 Ohya, Suruga-ku, 422-8529 Shizuoka, Japan

Yves Grohens* Laboratoire Polyme` res, Proprie´ te´ s aux Interfaces et Composites, UniVersite´ de Bretagne Sud, rue St. Maude´ BP 92116, 56321 Lorient Cedex, France ReceiVed June 1, 2005. In Final Form: NoVember 2, 2005 This investigation aimed to clarify the issue of whether polymer chains are entangled in ultrathin films spin-coated onto substrates. This was done using a fluorescence probe method to observe the behavior of two types of poly(methyl methacrylate) (PMMA), one having a carbazolyl (Cz) moiety (PMMA-Cz) and the other having an anthryl (At) moiety (PMMA-At). In both cases, the moiety fraction was 1 unit for 400 units of polymer. We prepared ultrathin films (thickness: 4-88 nm) on quartz substrates from PMMA-Cz, PMMA-At, and a mixture of the two using a spin-coating method. When the PMMA films prepared from the mixture of the two PMMAs were excited at 292 nm, which is preferentially absorbed by Cz rather than At, the Cz fluorescence was found to be quenched dramatically while the At fluorescence increased significantly. This effect is due to the proximity of the Cz to the At, which permits the transfer of excitation energy between them. The average distance between Cz and At can be calculated using the Fo¨rster mechanism. When the ultrathin film thickness was between 12 and 88 nm, the average distance was found to be 2 nm. This is much shorter than the radii of gyration of the polymers. From this it is clear that two polymer molecules in an ultrathin film do experience entanglement, as has been hypothesized. Thus, we conclude that the difference between certain properties of ultrathin films and the properties of the same materials in bulk are not induced by a decrease in the level of polymer chain entanglement.

Introduction The physical properties of ultrathin polymer films deposited on substrates are quite different from the properties of these same polymers in bulk quantities, a fact that has recently begun to attract the notice of investigators in a range of fields. Since Reiter, who first reported the difference between the dewetting behavior of bulk polystyrene (PS) and that of ultrathin (less than 20 nm) PS films,1 significant differences in many physical properties of ultrathin films have been demonstrated. Properties such as the glass transition temperature (Tg),2,3 the rate of crystallization,4 the polymer self-diffusion rate,5 and the permeability of gas in such films6 have all been shown to depend on the film thickness. Keddie2 and his colleagues, for example, demonstrated the dependence of Tg on film thickness for both PS and poly(methyl methacrylate) (PMMA) spin-coated onto silicon and gold. They showed that the Tg of 30 nm PMMA films on gold is 382 K, even though Tg ) 391 K for bulk PMMA.2b * Corresponding authors. E-mail: [email protected]. (H.I.); [email protected] (Y.G.). † Graduate School of Electronic Science and Technology. ‡ School of Education. (1) (a) Reiter, G. Europhys. Lett. 1994, 23, 579. (b) Reiter, G. Macromolecules 1994, 27, 3046. (2) (a) Keddie, J. L.; Jones, R. A. L.; Cory, R. A. Europhys. Lett. 1994, 27, 59. (b) Keddie, J. L.; Jones, R. A. L.; Cory, R. A. Faraday Discuss. 1994, 98, 219. (c) Keddie, J. L.; Jones, R. A. L.; Cory, R. A. Isr. J. Chem. 1995, 35, 21. (3) (a) Grohens, Y.; Brogly, M.; Labbe, C.; David, M.-O.; Schultz, J. Langmuir 1998, 14, 2929. (b) Grohens, Y.; Hamon, L.; Reiter, G.; Sodera, A.; Holl, Y. Eur. Phys. J. E 2002, 8, 217 (4) (a) Frank, C. W.; Rao, V.; Despotopoulou, M. M.; Pease, R. F. W.; Hinsberg, W. D.; Miller, R. D.; Rabolt, J. F. Science 1996, 273, 912. (b) Despotopoulou, M. M.; Frank, C. W.; Miller, R. D.; Rabolt, J. F. Macromolecules 1996, 29, 5797. (5) (a) Frank, B.; Gast. A. P.; Russell, T. P.; Brown, H. R.; Hawker, C. Macromolecules 1996, 29, 6531. (b) Zheng, X.; Rafailovich, M. H.; Sokolov, J.; Strzhemechcy, Y.; Schwarz, S. A.; Sauer, B. B.; Rubinstein, M. Phys. ReV. Lett. 1997, 79, 241. (6) Pfomm, P. H.; Koros, W. J. Polymer 1995, 36, 2379.

Similarly, we have found that the value of Tg for isotactic PMMA increased from 334 K in bulk solids to 383 K when it was spincoated onto a silicon wafer in an ultrathin film (thickness: ∼20 nm).3 Further clarification of the properties of ultrathin polymer films would be of considerable use in applications requiring the control of adhesion, wetting, or coating processes, and may permit the development of polymer materials with improved performance as photoresists or in artificial organs.7 The differences in the physical properties of ultrathin polymer films compared to those of bulk solids are a result of the existence of interfaces within the material that can induce confinement effects in the polymer chains. Polymer films are divided into three regions: (I) the interface between the substrate and the film; (II) the interface at the surface of the film (the interface between the air and the film); and (III) the intermediate region. Some authors claim that there is a high probability that the distribution and entanglement of polymer chains and/or free volumes in these three regions differ from one another.8 A thick film is dominated by the behavior of region III, and, in this case, the effect of the interface regions can be largely ignored. In contrast, for an ultrathin film, interface regions I and II cannot be neglected. Such a film has a thickness that is at most three times the radius of the gyration of an unperturbed polymer chain. It is not surprising, then, that ultrathin films show different properties from bulk films. Many papers have dealt with the question of why the value of Tg changes so dramatically for ultrathin films. The suggested explanations for the Tg behavior of these films seem to reduce to five possible (and probably interrelated) causes: (i) the effect of the attraction force between the substrate and the polymer (7) Itagaki, H. Polym. Appl. 2003, 52, 511. (8) (a) Baschnagel, J.; Binder, K. Macromolecules 1995, 28, 6808. (b) Forrest, J. A.; Mattsson, J. Phys. ReV. E 2000, 61, R53.

10.1021/la051432w CCC: $33.50 © 2006 American Chemical Society Published on Web 12/10/2005

Polymer Chain Entanglement in Ultrathin Films

chains,2 (ii) the enrichment of end-groups at the film surface,9 (iii) a decrease in the entanglement of polymer chains,1,10 (iv) novel types of motions, referred to as “sliding motions”, caused by the relaxation of polymer chain loops,11 and (v) density fluctuations based on a thermodynamical model.12 Let us consider the first few of these effects in turn. The first suggestion offered is that the magnitude of Tg will be affected by an interaction between the substrate and the polymer chains in a thin film. An example that demonstrates the presence of this interaction very clearly is the case of stereoregular PMMA films spin-cast onto silicon and aluminum surfaces. Monitoring the carbonyl peak of the infrared reflection absorption provides a convenient method for tracking the interactions between the two substances.3 Moreover, Fryer et al. showed that they were able to modify the surface energies, γ, of the substrate surfaces by spin-coating them with PS and PMMA.13 At high values of γ, the Tg values of the PS and PMMA ultrathin films were higher than the values for these substances in bulk, and they increased monotonically with increasing γ. In support of this result, the molecular dynamics simulations by Torres et al. demonstrated that the Tg values of ultrathin films less than 60 nm thick increase as the intermolecular potential between the polymer chains and the substrate increases.14 They conclude that the increase in Tg is due mainly to the force of attraction between the polymer chains and the substrate. In contrast, the mechanisms described under points ii and iii above are expected to cause a decrease in Tg. Even if the polymer chain end-groups are not modeled as having any strong interaction force, simulations using both molecular dynamics15 and the Monte Carlo method16 demonstrate that the chain end-groups localize at the free surface and/or at the interface with the substrate. Mayes, using a simple scaling analysis, surmised that such end enrichment at the film surface could have a marked influence on properties such as Tg, whose depletion region is within a distance nearly equal to the radius of gyration from the surface.9 In the wake of this analysis, several experiments have established that end-groups are aggregated at the free surface of thick films.17,18 Kajiyama et al. used lateral force microscopy to demonstrate that the surface Tg of thick films was much lower than that of the bulk sample and that this depletion of the surface Tg was due to the localization of chain end-groups.18 There is no doubt that the enrichment of end-groups at the film surface is one of the most attractive explanations for the decrease in the value of Tg for thick films. However, Tsui et al. were able to show that the same cannot be said for very thin films. They found that, although the chain ends were segregated to the surface, they had little effect on the Tg of a film with a small thickness (15 nm).19 Furthermore, Briggs et al. showed that the fraction of chain ends at the surface was too small to have a drastic (9) Mayes, A. M. Macromolecules 1994, 27, 3114. (10) Brown, H. R.; Russell, T. P. Macromolecules 1996, 29, 798. (11) De Gennes, P. G. Eur. Phys. J. E 2000, 2, 2001. (12) Long, D.; Lequeux, F. Eur. Phys. J. E 2001, 4, 371. (13) Fryer, D. S.; Peters, R. D.; Kim, E. J.; Tomaszewski, J. E.; de Pablo, J. J.; Nealey, P. F.; White, C. C.; Wu, W. L. Macromolecules 2001, 34, 5627. (14) Torres, J. A.; Nealey, P. F.; de Pablo, J. J. Phys. ReV. Lett. 2000, 85, 3221. (15) Bitsanis, I.; Hadziioannou, G. J. Chem. Phys. 1990, 92, 3827. (16) Kumar, S. K.; Vacatello, M.; Yoon, D. Y. J. Chem. Phys. 1988, 89, 5206. (17) (a) Zhao, W.; Zhao, X.; Rafailovich, M. H.; Sokolov, J.; Composto, R. J.; Smith, S. D.; Satkowski, M.; Russell, T. P.; Dozier, W. D.; Mansfield, T. Macromolecules 1993, 26, 561. (b) Botelho do Rego, A. M.; Lopes da Silva, J. D.; Rei Vilar, M.; Schott, M.; Petitjean, S.; Je´roˆme, R. Macromolecules 1993, 26, 4986. (c) Affrossman, S.; Hartshorne, M.; Je´roˆme, R.; Pethrick, R. A.; Petitjean, S.; Rei Vilar, M. Macromolecules 1993, 26, 6251. (18) (a) Kajiyama, T.; Tanaka, K.; Takahara, A. Macromolecules 1995, 28, 3482. (b) Tanaka, K.; Taura, A.; Ge, S.-R.; Takahara, A.; Kajiyama, T. Macromolecules 1996, 29, 3040. (c) Tanaka, K.; Takahara, A.; Kajiyama, T. Macromolecules 1997, 30, 6626. (19) Tsui, O. K. C.; Zhang, H. F. Macromolecules 2001, 34, 9139.

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Figure 1. Structure of PMMA-Cz and PMMA-At. The terms x and y represent the fraction of the probe group (molar fraction).

impact on the observed surface Tg.20 It appears, then, that, although the depression of Tg in ultrathin films due to effect ii should never be neglected, it cannot, either alone or in simple combination with effect i, account for the significant change in Tg in these films. We now move on to consider the third proposed cause of the observed change in Tg: a decrease in the entanglement of polymer chains. Brown and Russell assumed such a decrease near the interface of a film, and were able to demonstrate that this would induce a decrease in Tg.10 A demonstration of the effect is therefore of considerable interest since it could constitute one of the main mechanisms in the observed changes in Tg. Ultrathin films, being less than ∼30 nm thick, are usually prepared from dilute solution with concentrations less than 0.1 wt %. There is evidence that no polymer chains are entangled with one another in a dilute solution with a concentration lower than some critical concentration C*.21,22 As has been reported in freeze-dried systems,22 fast evaporation of the solvent during the spin-coating process is supposed to hinder any subsequent entanglement during the deposition of the films onto the substrate. However, even though authors have concluded that the disentanglement of macromolecular chains should lead to Tg variation in freeze-dried or in thin PS films, they do not provide any direct evidence for such disentanglement in ultrathin films. In the present work, we used a fluorescent probe to investigate the extent to which macromolecules are entangled in ultrathin films. This method is a powerful and efficient technique that uses the response of a probe molecule to provide information on the microenvironment at the molecular level.23 We employed two types of PMMA molecules as our probes: PMMA-Cz, which has a carbazolyl (Cz) moiety, and PMMA-At, which has an anthryl (At) moiety. The fraction of each moiety of PMMA-Cz and PMMA-At was almost 1 unit per polymer molecule (see Figure 1). We prepared ultrathin films from the PMMA-Cz, the PMMA-At, and a mixture of the two. By measuring the energy transfer efficiency, we were able to determine the average distance between the Cz and the At in the film prepared using a mixture of the two molecules. If the PMMA chains are entangled with one another, this average distance should be short. Alternatively, if the distance between the probe molecules is much larger than the radii of gyration for these molecules, this would imply that the PMMA molecules are not significantly entangled. This is the (20) Bliznyuk, V. N.; Assender, H. E.; Briggs, G. A. D. Macromolecules 2002, 35, 6613. (21) (a) Huang, D.; Yang, Y.; Zhuang, G.; Li, B. Macromolecules 1999, 32, 6675. (b) Huang, D.; Yang, Y.; Zhuang, G.; Li, B. Macromolecules 2000, 33, 461. (22) Bernazzani, P.; Simon, S. L.; Plazek, D. J.; Ngai, K. L. Eur. Phys. J. E 2002, 8, 201. (23) (a) Itagaki, H.; Horie, K.; Mita, I. Prog. Polym. Sci. 1990, 15, 361. (b) Itagaki, H. In Experimental Methods in Polymer Science: Modern Methods in Polymer Research and Technology; Tanaka, T., Ed.; Academic Press: New York, 2000; Chapter 3, p 155.

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Figure 2. Preferred orientation of a sample in a spectrofluorometer for fluorescence measurements of a film cast on a substrate. Table 1. Characterization of Each PMMA Type Showing the Fraction of Each Fluorescent Probe Group Present sample

molar ratio of probe groups (%)

Mw

Mw/Mn

PMMA-Cz PMMA-Cz-h PMMA-At PMMA-At-h

0.26 0.92 0.35 1.60

45, 600 47, 300 43, 800 51, 800

1.53 1.59 1.50 1.69

first direct investigation to prove whether polymer chains are entangled in ultrathin films. Experimental Section Materials. The samples used in this experiment were kindly supplied by Prof. R. E. Prud’homme of Universite´ de Montre´al. The synthesis of the labeled PMMA was performed in anhydrous tetrahydrofuran at room temperature to attach the carbazolyl and anthryl moieties onto PMMA by reaction with the ester side groups.24 Each probe group is assumed to be randomly distributed in each polymer molecule. The structures of the two types of polymers are shown in Figure 1, and the characteristics of the PMMA samples are summarized in Table 1. The numbers of each probe unit (namely, Cz and At) and the other methyl methacrylate (MMA) units are estimated to be as follows: PMMA-Cz, 1.18:452 (Cz/MMA); PMMA-Cz-h, 4.28:461 (Cz/MMA); PMMA-At, 1.52:433 (At/ MMA); PMMA-At-h, 8.05:495 (At/MMA). Their molecular weights were measured at 40 °C on a Tosoh HLC-8120 GPC system equipped with two TSK gel superHM-M columns using tetrahydrofuran as an eluting solvent. Twelve standard PS samples were used to calibrate the molecular weight as a function of the elution volume. The fraction of the carbazolyl group present in the PMMA-Cz sample and that of the anthryl group present in the PMMA-At sample were determined by measuring the UV absorption characteristics. N-Methylcarbazole was employed as a monomer model for the PMMA-Cz, and 9-methylanthracene was used for the PMMA-At. Information on the tacticity of both PMMAs was obtained from 1H NMR measurements, and was found to be r(racemo)r: 50, m(meso)r: 35, and mm: 15 (%). The PMMA films for the fluorescence measurements were prepared on quartz disks using a spin-casting method from solutions of chloroform with PMMA concentrations ranging from 0.040 to 1.0% (wt/wt). The disks were spun at 2000 rpm and dried under vacuum for more than 3 days at 40 °C. A second set of films were prepared on silicon wafers in the same way for measurements of film thickness using an ellipsometer. More than four films at each concentration in each of the two sets were prepared to ascertain the reproducibility of both the fluorescence and film thickness measurements. Sample Characterization Measurements. UV absorption spectra were measured on a Shimadzu UV-2200 UV-Vis spectrophotometer. Fluorescence spectra and fluorescence excitation spectra were measured on a Hitachi F-4500 spectrofluorometer at 25 °C. The films were set at 45° to the exciting beam as shown in Figure 2. The fluorescence measurements for dilute aerated solutions of PMMACz and PMMA-At were carried out in a quartz cell with an optical path length of 1 mm. This cell was also set at 45° to the exciting beam. The film thicknesses were measured on a Mizojiri Kogaku DHA-OLXS automatic ellipsometer. (24) Zhao, Y.; Prud’homme, R. E. Polym. Bull. 1991, 26, 101.

Investigation of Polymer Entanglement. Measurements of the average distance between the Cz of the PMMA-Cz and the At of the PMMA-At were undertaken in the following way: First, three types of ultrathin films were spin-coated onto substrates of equal thickness: a pure PMMA-Cz film, a pure PMMA-At film, and a film made with a mixture of 50% (w/w) PMMA-Cz and 50% (w/w) PMMA-At (the “PMMA-mix” film). Next, we measured the Cz fluorescence intensities of all three film types by exciting them at a wavelength readily absorbed by Cz, but not by At. Finally, by comparing the intensities of the Cz fluorescence, we were able to examine whether the Cz fluorescence is quenched in a PMMA-mix film. The measurement of the fluorescence spectra, which would typically be found using a transmission measurement such as the one illustrated in Figure 2, was complicated by the fact that silicon wafers such as those that are generally used as the substrates for ultrathin films are not transparent. An alternative method could involve a measurement of the reflected fluorescence, but it was found that, in this case, the spectra were distorted due to the interference between the fluorescence from the film and the light reflected from the surface of the substrate. It was decided that a quartz disk would be the best substrate for the fluorescence measurements. This choice, however, leads to its own problems. The very quality that makes quartz a better substrate for fluorescence measurements, its transparency, means that we cannot measure the thickness of the films spin-coated onto it. The opaque silicon substrate is preferable for thickness measurements. Ultimately, films were prepared under identical conditions on both silicon and quartz substrates so that the various measurements necessary for the investigation could be made effectively.

Results and Discussion Thickness of PMMA-Cz and PMMA-At Ultrathin Films. As has already been discussed, although we used quartz substrates for the PMMA films used for the fluorescence measurements, we were unable to use ellipsometry to measure the thickness of these ultrathin films when they had been spin-coated on such a transparent material. The spin-casting method, however, permits the preparation of films with a high degree of reproducibility, and spontaneous oxidation ensures that the surface of quartz is chemically similar to the surface of silicon, which is covered with a layer of silicon oxide. It is therefore reasonable to expect that the relationship between the concentration of the polymer solution used and the thickness of the films produced will be the same whether the films are spin-coated onto silicon or quartz. We therefore prepared an identical set of PMMA films on silicon wafers and measured their film thickness by ellipsometry. Figure 3 shows that, for the same set of spin-coating conditions, the values for the thickness are proportional to the concentration of the PMMA solutions used as the base for the films. The reproducibility of these results was found to be quite high. We prepared ultrathin films using PMMA-Cz, PMMA-At, and the PMMA-mix and found that there was no significant difference in the thicknesses, provided the concentrations were at about the same level. When combined with the known similarity between the surface oxidation of quartz and silicon, the fact that the data presented in Figure 3 was found to have a coefficient of determination very close to 1 increased our confidence in the decision to assume that the thickness of a film spin-coated onto a silicon wafer with a silicon oxide surface layer will be the same as that of a film deposited on a quartz disk.25 The relationship established in Figure 3 was used to calculate the thickness of films prepared from PMMA solutions with concentrations higher than 0.070% (w/w). For films prepared from 0.040% (w/w) (25) It is clear that the structure of the surface of quartz is not in fact the same as that of silicon. This treatment is however sufficient for our purpose, which was simply to obtain reasonable values of the film thickness.

Polymer Chain Entanglement in Ultrathin Films

Figure 3. Relationship between the concentration of PMMA solution (c % (w/w)) and film thickness for films prepared using a spincasting method (2000 rpm) on silicon wafers. For each concentration, films were prepared using either PMMA-Cz, PMMA-At, or PMMAmix solutions. The results for all three solutions were found to follow the same trend. All are included on the graph, which was shown to obey the relationship (solid line, r2 ) 0.995) thickness ) 84.85 × concentration + 3.00.

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Figure 5. Dependence of the peak intensity of Cz fluorescence from PMMA-Cz ultrathin films on quartz substrates on film thickness. The excitation wavelength was 292 nm.

Figure 6. Fluorescence spectra from 12 nm thick PMMA-mix, PMMA-Cz, and PMMA-At films on quartz disks. The excitation wavelength was 292 nm in each case. Each presented spectrum is an average of 3 to 4 measured spectra. Figure 4. Fluorescence spectra of three PMMA-Cz films spincoated on quartz from a 0.0402% (w/w) chloroform solution (film thickness ) 4.2 nm). The excitation wavelength was 292 nm.

solutions, the film thickness on quartz was determined by measuring the thickness of 4 films prepared on silicon prepared from the exact same solutions. Fluorescence Behavior of PMMA-Cz and PMMA-At Ultrathin Films. Figure 4 shows the fluorescence spectra of PMMA-Cz ultrathin films on quartz disks prepared from a 0.040% chloroform solution. For each film, the thickness is assumed to be 4.2 nm. Three films prepared under the same conditions showed the same fluorescence spectra with the same intensities, verifying the reproducibility of the films. We prepared PMMA films on quartz from chloroform solutions with different PMMA concentrations (i.e., we prepared films of varying thickness). Figure 5 shows the dependence of the peak intensity of the Cz fluorescence signal on the thickness of the PMMA-Cz films. The dependence was found to be directly proportional. Both the reproducibility of the film thickness and the linearity of the intensity as a function of thickness were also ascertained for PMMA-At films. The fluorescence spectra of the PMMA-mix films prepared with the same concentrations were also found to be identical to one another and demonstrated fluorescence peaks corresponding to both Cz and At. Since the present experiments were done in the aerated atmosphere, there is a possibility that the excited states of chromophores at the surface layer suffer from oxygen attack more than those deep inside the film. If the effect should be high, the fluorescence intensities of the chromophores in thinner films would decrease greatly. However, the dependence of the peak intensities of Cz (PMMA-Cz) and At (PMMA-At) fluorescence

on film thickness is found to be the same down to 4.2 nm. From these results, we concluded that (i) both the Cz of the PMMA-Cz and the At of the PMMA-At are dispersed uniformly in the ultrathin films, (ii) the fluorescence intensities of Cz and At are proportional to the thickness of the films, and (iii) we do not have to take into account surface quenching effects explicitly in the case of examining fluorescence quenching ratios of the films as thin as 4.2 nm. Fluorescence Behaviors of PMMA-Mix Ultrathin Films. Figure 6 shows the fluorescence spectra of PMMA-mix, PMMACz, and PMMA-At films with the same thickness (12 nm). Since the thickness was kept constant, the concentrations of Cz and At in the PMMA-mix films were nearly half of those in the pure PMMA-Cz and PMMA-At films. As a result of this, we scaled the concentration of Cz in the PMMA-mix results by a factor R such that R ) MPMMA-Cz/Mmix, where MPMMA-Cz and Mmix are the concentrations of PMMA-Cz in the solutions used for making the two types of films, respectively. Note that R is almost 2.0 in every case. All the spectra shown in Figure 6 are in fact the result of taking an average of either 3 or 4 spectra, with an excitation wavelength of 292 nm. The excitation wavelength was chosen because it is the peak wavelength for Cz absorption but is not readily absorbed by At. We expect the At spectrum, therefore, to be visible but lower in intensity. From the combined results, it is clear that the fluorescence peaks for both Cz (which occur at 348 and 362 nm) and for At (at 392, 414 and 440 nm) are in fact readily identifiable. As expected, the intensity of the fluorescence spectrum for PMMA-At is quite low. Even after adjustment to account for the variation in Cz concentration, it is clear that the Cz fluorescence in the PMMA-

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using a theory developed by Fo¨rster26 and Galanin.27 Their model, which is called the Fo¨rster mechanism, is based on the assumption that the most significant contribution to the interaction term comes from the dipole transition moment between a donor and an acceptor. The time profile of the donor fluorescence after a δ-pulse excitation is written in the following form when the molecules are fixed in an inert solid film:26

ID(t) ) I0 exp[-t/τD] (in the case without any acceptors) (2) IDA(t) ) I0 exp[-t/τD - 2ξxt/τD] (in the case with acceptors around a donor molecule) (3) Figure 7. Dependence of fluorescence quenching ratio for Cz in PMMA-mix films on film thickness. The excitation wavelength was 292 nm, and the values were obtained by averaging the Cz intensities for 3 to 4 films of the given thickness each time.

mix spectrum in Figure 6 is considerably weaker than that in the spectrum from the pure PMMA-Cz film of the same thickness. This indicates that the Cz fluorescence was significantly quenched in the ultrathin films created from the mixture of PMMA-Cz and PMMA-At. In contrast, the At fluorescence increased in the film with the mixed composition. We contend that these changes in the spectra are due to a singlet energy transfer from the Cz to the At in the PMMA-mix film. In an effort to quantify this result, we defined a “quenching ratio” for the Cz fluorescence. Let the peak intensity of the Cz fluorescence from a film prepared using only PMMA-Cz be IPMMA-Cz and that from a film prepared using PMMA-mix be Cz Imix Cz . We have already observed that, for films of identical thickness and Cz concentration, Imix Cz is significantly smaller than . We therefore define the quenching ratio so that it has IPMMA-Cz Cz the form PMMA-Cz Quenching ratio ) 1 - RImix Cz /ICz

where ID(t) and IDA(t) are the fluorescence intensities of the donor at time t without and with acceptors, respectively, τD is the unquenched lifetime of the donor, I0 is a constant corresponding to the concentration of the donor, and ξ corresponds to the local concentration of the acceptors around a donor molecule. ξ can be expressed as eq 4

()

ξ ) A0

3

(4)

where R0 is a critical radius known as the Fo¨rster radius, r is the average distance between the donor and the acceptor, and A0 is a constant. When r ) R0, the probability that the excited energy of the donor transfers to an acceptor molecule is 50%. Since the fluorescence intensities of the donor can be calculated by the integration of each time profile over the whole time range, both in the cases with and in those without the acceptor molecules, the quenching ratio should be described as eq 5

∫0∞ IDA(t)dt Quenching ratio ) 1 - ∞ ∫0 ID(t)dt

(1)

where R is the ratio of the concentration of Cz in a film of only PMMA-Cz to that of Cz in a film of PMMA-mix. If this value changes with the PMMA-mix film thickness, then the spatial distribution of Cz and At in the film can be assumed to change as well. In particular, if the quenching ratio should decrease substantially as the film thickness decreases, then the average distance between the Cz of the PMMA-Cz and the At of the PMMA-At can be assumed to have become longer. Figure 7 shows the dependence of the quenching ratio on film thickness. This clearly demonstrates that the distribution of Cz and At does not change in PMMA-mix films between 12 and 88 nm in thickness. Notice that, in general, films with a thickness of 88 nm or more have the same properties as bulk films. From this, it can be concluded that the level of entanglement of PMMA-Cz and PMMA-At in PMMA-mix films as thin as 12 nm thick is the same as that of PMMA molecules in bulk films. Estimation of Average Distance between Cz of PMMA-Cz and At of PMMA-At. Figure 7 demonstrates the similarity in the level of entanglement of polymer molecules in bulk compared to the levels in films as thin as 12 nm. In this section, we would like to estimate the average distance between the Cz and the At in PMMA-mix films. The observed quenching in the Cz intensity is the result of an excitation transportation process that depends on the coupling strength of a donor Cz and an acceptor At. This energy transport, which is due to Coulombic resonance interactions, is described

R0 r

) xπξ exp(ξ2)[1 - Erf(ξ)]

(5)

∫0ξ exp(-x2)dx

(6)

where

Erf(ξ) )

2 xπ

Bennett et al.28 showed that the energy transfer process between two chromophores in polymer films was expressed as eqs 3 and 5; namely, the steady-state measurements gave the same results obtained by using transient fluorescence measurements. Mataga et al.29 experimentally demonstrated that the energy transfer from pyrene to perylene in PMMA films followed the above formula of the Fo¨rster mechanism: the experimental value of R0 obtained from the energy transfer taking place in the PMMA films was found to be identical with the value obtained from both the fluorescence spectrum of the donor and the absorption spectrum of the acceptors in fluid solutions. Therefore, we can use the above Fo¨rster formula to describe the energy transfer between a donor and an acceptor in bulk PMMA films, since this validity is widely accepted. Figure 7 shows that the energy transfer from a Cz of PMMA-Cz to an At (26) (a) Fo¨rster, Th. Naturwissenschaften 1946, 33, 166. (b) Fo¨rster, Th. Discuss. Faraday Soc. 1959, 27, 7. (27) Galanin, M. D. Zh. Eksp. Teor. Fiz., JETP 1955, 1, 317. (28) Bennett, R. G.; Schwenker, R. P.; Kellog, R. E. J. Chem. Phys. 1964, 41, 3040. (29) (a) Mataga, N.; Kobashi, H.; Okada, T. Chem. Phys. Lett. 1967, 1, 133. (b) Mataga, N.; Kobashi, H.; Okada, T. J. Phys. Chem. 1969, 73, 370.

Polymer Chain Entanglement in Ultrathin Films

Figure 8. Average distances between Cz and At in PMMA-mix films determined from the level of Cz fluorescence quenching using eq 5.

of PMMA-At in PMMA-mix is constant among the films that are 12 and 88 nm thick. The PMMA-mix with a thickness of 88 nm is assumed to be under the same circumstance as bulk PMMA films in which the isotropic energy transfer should take place, as in the case described by eqs 3 and 5.28,29 Thus, we calculated average distance r using eq 5:30 in the model case where the donor is N-methylcarbazole and the acceptor is 9-methylanthracene, R0 is 2.875 nm.31 The result of the calculations of this average distance appears in Figure 8. The values of r were calculated to be 1.9 nm in PMMA-mix films that are 12-88 nm thick. Here are two problems to consider in the present system. One is that the energy transfer process becomes not only time dependent but also site dependent when the thickness of thin films is comparable with the Fo¨rster radius. The calculation of average distance r for the films that are thinner than 10 nm is considered to be strongly dependent on the model described below, and we have to be more careful when estimating them. Another problem is that the energy migration among Cz chromophores could take place and would influence the values of the quenching ratio because R0 for energy migration between N-methylcarbazole molecules, a model of the Cz of PMMA-Cz, is relatively large (2.134 nm).31 Regarding the first problem, Klafter and Blumen32 extended the equation describing the time dependence of a donor intensity to fractal systems. Their equation has been effectively applied to the systems having heterogeneous distributions of donors in interface regions.33 Moreover, the dimensionality is another important problem. By using energy transfer processes, quite a few authors have obtained important information on microenvironments of Langmuir-Blodgett (LB) polymer films where chromophores are distributed in each two-dimensional plane that is deposited.34,35 In particular, Ito et al.35 successfully estimated the degree of disordering of layered LB films by analyzing the decay curve of donor fluorescence using a theoretical model in which the chromophores distributed according to a Gaussian function in the direction of the normal plane. Taking into consideration these works, it is difficult to determine the cause for the decrease in the quenching ratio observed for films thinner (30) A0 in eq 4 was determined so as to give a quenching ratio of 0.5 when r ) R0. (31) Berlman, I. B. Energy Transfer Parameters of Aromatic Compounds; Academic Press: New York, 1973. (32) Klafter, J.; Blumen, A E. J. Chem. Phys. 1984, 80, 875. (33) (a) Tcherkasskaya, O.; Spiro, J. G.; Ni, S.; Winnik, M. A. J. Phys. Chem. 1996, 100, 7114. (b) Farinha, J. P. S.; Martinho, J. M. G.; Kawaguchi, S.; Yekta, A.; Winnik, M. A. J. Phys. Chem. 1996, 100, 12552. (c) Rharbi, Y.; Yekta, A.; Winnik, M. A.; DeVoe, R. J.; Barrera, D. Macromolecules 1999, 32, 3241. (34) For example, (a) Yamazaki, I.; Tamai, N.; Yamazaki T. J. Phys. Chem. 1987, 91, 3572. (b) Yatsue, T.; Miyashita, T. J. Phys. Chem. 1995, 99, 16047. (35) Ohmori, S.; Ito, S.; Yamamoto, M. Macromolecules 1991, 24, 2377.

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than 10 nm. It may be due to the distance r becoming longer or due to the distribution of the chromophores becoming heterogeneous. Regarding the present trial to get information on the entanglement of polymer molecules, suffice it to say that (i) the average distance between the Cz of PMMA-Cz and the At of PMMA-At is about 2 nm in PMMA-mix films that are more than 12 nm thick, and (ii) it is not so long, even in the ultrathin films that are 4 nm thick. Concerning the second problem, Ito et al.36 reported that the energy migration took place quite efficiently among Cz groups in a layered structure of LB films of poly(isobutyl methacrylate) having Cz as the side-chain groups, although the orientation of Cz groups would be different among LB films and ultrathin films on substrates. To consider the effect of the energy migration among Cz groups, we prepared ultrathin films that were 11-12 nm thick from the different PMMA samples shown in Table 1, and measured the quenching ratio of Cz when the concentrations of Cz and At in the films were changed. The results are summarized in Table 2. We would not be able to get the correct information on r if the energy migration among the Cz groups is so efficient that the excitation energy absorbed by Cz can almost always reach At, even if r is very large. However, the results shown in Table 2 indicate that the energy transfer from Cz to At is dependent more strongly on the distance between Cz and At than the distance between the Cz groups. For example, if the energy migration among the Cz groups in the films prepared from PMMA-Czh/PMMA-At takes place quite efficiently, its quenching ratio should be identical with the quenching ratio of PMMA-Cz/ PMMA-At (namely, PMMA-mix so far). Since the R0 value from Cz to At (2.875 nm) is larger than that from Cz to Cz (2.134 nm),31 the energy transfer efficiency would be accelerated more by the energy migration among the Cz groups. However, the quenching ratio of the films prepared from PMMA-Cz-h/PMMAAt is quite low. It is due to the decrease in the fraction of local At concentration per one Cz group, namely, the increase in the average distance between Cz and At. On the other hand, the quenching ratio of the films prepared from PMMA-Cz/PMMAAt-h is higher than that of PMMA-Cz/PMMA-At. It is quite reasonable because the local concentration of the acceptor increased so much: PMMA-At-h is assumed to give enough concentration of At to catch almost all excitation energy absorbed by any Cz groups when each PMMA molecule is entangled more or less. It can never be denied that the energy migration among Cz in the present ultrathin films takes place, but the short average distance between Cz and At is the main reason for the high efficiency of the energy transfer between Cz and At. Entanglement of Polymer Molecules in Ultrathin Films. Our method using PMMA-Cz and PMMA-At showed that the energy transfer efficiency is constant in ultrathin films that are 12-88 nm thick. It demonstrates that the level of entanglement of PMMA-Cz and PMMA-At in PMMA-mix films as thin as 12 nm thick is the same as that of PMMA molecules in bulk films. Although based on a simple model, the average distance r in these films is about 2 nm, and this result gives a clear indication of significant levels of entanglement between the PMMA-Cz and the PMMA-At in films produced using a mixture containing equal concentrations of these polymers. The end-to-end distances for unperturbed states of PMMA-Cz and PMMA-At are calculated to be 13.7 and 13.4 nm, respectively, while the radii of gyration are 5.6 and 5.5 nm. Compared with these values, a distance of 2 nm is so short that a PMMA-Cz and a PMMA-At can definitely be said to be entangled in PMMA-mix films on quartz. Even for (36) Ito, S.; Ohmori, S.; Yamamoto, M. Macromolecules 1992, 25, 185.

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Itagaki et al.

Table 2. Quenching Ratio of Cz in the Thin Films Prepared from PMMAs Having Different Amounts of Cz and At Together with the Calculated Values of r Using Eq 5

samples

Cz (unit per polymer)

At (unit per polymer)

film thickness (nm)

quenching ratio

r (nm)

PMMA-Cz/PMMA-At PMMA-Cz/PMMA-At-h PMMA-Cz-h/PMMA-At PMMA-Cz-h/PMMA-At-h

1.18 1.18 4.28 4.28

1.52 8.05 1.52 8.05

11.6 11.4 11.4 11.5

0.839 0.947 0.691 0.952

1.95 1.53 2.35 1.51

films assumed to be only 4 nm thick, where the value of r is predicted to be higher, the average distance between the two structures is still smaller than 3 nm. Although the energy transfer process may not be correctly expressed by our simple model, it is clear that the Cz of PMMA-Cz and the At of PMMA-At should be so close that the energy transfer can occur. As a reference, we also measured the fluorescence spectrum of a 0.30% solution of PMMA-mix in chloroform (Figure 9). We compared this with the spectrum from films made from this same solution, which had a thickness of 29 nm, and were made, as were the rest of the films, using a spin-casting method. The concentrations of Cz and At were so low in the solution that the

Figure 9. Fluorescence spectrum of (1) chloroform solution of 0.301% PMMA-mix in a quartz cell with an optical path length of 1 mm and (2) the ultrathin film on quartz spin-coated from the same solution (film thickness ) 29 nm). The excitation wavelength was 292 nm, and both spectra were normalized to the Cz fluorescence peak.

average distance between them was too long for any excitation energy to be transferred. This result is consistent with other results21 that demonstrated that polymer chains remain independent from one another in dilute solutions with concentrations as high as 0.1 wt %. We therefore concluded that the entanglement of these PMMA polymers is produced during the spin-coating process itself. In conclusion, we have demonstrated that there is entanglement of PMMA molecules in films that are ∼4 nm thick, even though there was no evidence of molecular entanglement in the dilute solutions used for spin-casting films onto their quartz substrates. Now that the entanglement of polymer molecules is verified, we can conclude that the slight Tg decrease (10 °C) which occurs in ultrathin films of atactic PMMA on gold2 is not induced by a modification of the level of polymer chain entanglement. However, the huge Tg deviation observed in freely standing PS37or stereoregular PMMA3 cannot be extrapolated from these data. Further investigation based on the methodology developed here is required in order to come to a definite conclusion about the importance of molecular entanglement on the observed large variations in Tg in ultrathin films. Acknowledgment. We wish to express our sincere gratitude to Professor Michiharu Tabe and Dr. Takeshi Mizuno of Shizuoka University for their kind suggestions relating to the use of ellipsometry in our thickness measurements.We also acknowledge Professor Prud’homme from the Universite´ de Montre´al for supplying the labeled PMMA. LA051432W (37) Forrest, J. A.; Dalnoki-Veress, K.; Dutcher, J. R. Phys. ReV. E 1997, 56, 5705.