The glass transition in thin polymer films

Transcription

1 Advances in Colloid and Interface Science Ž The lass transition in thin polymer films James A. Forrest a,, Kari Dalnoki-Veress b,1 a Department of Physics and Guelph Waterloo Physics Institute, Uni ersity of Waterloo, Waterloo, Ontario, Canada N2L 3G1 b Department of Physics and Astronomy, Uni ersity of Sheffield, S3 7RH Sheffield, UK Received 29 May 2000; accepted 18 Auust 2000 Abstract In this article, e present a detailed account of important recent developments in the rapidly evolvin area of lass transitions in thin polymer films. We revie the case of polymer films supported by substrates, and sho that a definite experimental consensus exists. We consider recent results from experimental studies of free-standin films of polystyrene. These studies have provided a thorouh quantification of the behavior of lass transition anomalies in free-standin polymer films, and have served to motivate recent attempts at theoretical descriptions. We introduce and examine models, hich have been proposed to explain the experimental observations and discuss the sinificance of these models Elsevier Science B.V. All rihts reserved. Keyords: Glass transition; Thin polymer films; Dynamics in confinement Contents 1. Introduction Measurin the lass transition in thin films The lass transition in supported polymer films Measurements of the lass transition in supported films Resolvin controversy in thin film T studies Other probes of dynamics in thin polymer films Correspondin author. Ž. address: jforrest@uaterloo.ca J.A. Forrest. 1 Present address: McMaster University, Hamilton, Ontario, Canada L8S 4M $ - see front matter 2001 Elsevier Science B.V. All rihts reserved. Ž. PII: S

2 168 ( ) J.A. Forrest, K. Dalnoki-Veress Ad ances in Colloid and Interface Science The lass transition in free-standin films T for free-standin films ith M Importance of annealin history T for free-standin films ith M Models used to describe T data Layer model ith dynamic heteroeneities Possible implications for the lenth scale of lass transition dynamics The slidin model of de Gennes for hih M free-standin films Future issues Conclusions Acknoledements References Introduction Glass formin substances are ubiquitous materials. Oranic liquids, polymers, and even metals can all undero a lass transition and form a lassy rather than crystalline solid. Despite the obvious technoloical importance of lass formin materials, it has to be noted that the lass transition itself, thouh ell characterized, is enerally not ell understood. The lack of understandin is reflected in the fact that there are no theories hich even claim to offer a description of all aspects of the dynamics of lass formin materials. The ell-knon free volume model of Cohen and Turnbull 1 is an intuitive and appealin picture, but the approach is phenomenoloical in nature and the free volume is not riorously defined. The mode couplin theory of Sjoren and Gotze 2 is successful at describin the dynamics of many lass formers at hih temperatures, but fails to describe the dynamics at temperatures near the calorimetric lass transition. Thermodynamic theories of the lass transition also exist 3, but except for a fe instances 4, do not readily lead to a description of the dynamics. One concept, hich is often used in the description of lass transition dynamics, is the idea of co-operative motion. The basic idea behind the approach, first introduced empirically by Adam and Gibbs 5, is that as the temperature in a lass formin material is brouht near the lass transition temperature, individual particle motion is frozen out. The result is that the only structural rearranements, hich may occur must involve the collective movement of many particles, and the lenth scale for co-operative dynamics must be temperature-dependent, increasin as the temperature is loered. In a more riorous approach, Edards and Vilis 6 developed an exactly solvable model system for lass transition dynamics and ere able to sho that co-operative motion alone as enouh to ive rise to a Voel Fulcher temperature dependence of relaxation times on temperature. Recent computer simulations 7,8 have revealed the existence of co-operative motion here particle motion occurs in strin-like clusters. The dimension of such clusters is fractal, but 1, and the number of units in a cluster as found to increase ith decreasin temperature. Computer simulations have also revealed a stron dy-

3 ( ) J.A. Forrest, K. Dalnoki-Veress Ad ances in Colloid and Interface Science namic heteroeneity in lass formin materials. The co-operative motion is found to exist only ithin mobile clusters, and the lenth scale for this dynamic heteroeneity is expected to be closely related to that of co-operative motion and is found to have qualitatively the same temperature dependence. While most simulations have involved simple particles interactin throuh a Lennard Jones potential, similar results have been found for polymers. A roin lenth scale for dynamics has been observed in molecular dynamics simulations of a polymer melt 9, as has a clusterin of mobile monomer units 10. From the evidence provided by theory and simulation it is reasonable to define a lenth scale Ž T., for the dynamics of lass formin materials. Our picture of a lass formin liquid near T, is one hich is on averae homoeneous, but instantaneously heteroeneous, and consists of some reions hich are more liquid-like and others hich are more solid-like. These reions are not necessarily stronly correlated to density fluctuations. Since these reions are structurally indistinuishable, and differ only in their dynamics, there is no hope to use scatterin methods to determine the lenth scale Ž T.. Instead the only ay to ascertain the existence of such a lenth scale is throuh the use of finite size effects. The central idea behind finite size effects is easily described. The sample is confined to a size D. At hih enouh temperatures Ž T. D, the dynamics of the confined system ill be the same as the bulk system. As the temperature is loered, Ž T. increases and eventually the condition Ž T. D, ill be reached. When Ž T. D, the confined system ill exhibit anomalous dynamics compared to the correspondin bulk system. The ay the dynamics of the confined system ill be affected depends stronly on the boundary conditions of the system. From the concept of co-operative motion, it is clear that if the molecules on the boundary are held fixed Ž stronly attractive interaction in an experiment., then the confined system ill exhibit much sloer dynamics than the bulk system or may even be completely arrested. Alternatively, if the molecules on the boundary have a hih deree of freedom Ž such as in the experimental case of a free surface., then the dynamics of the confined system ill be faster than that of the bulk system. The first comprehensive study of lass formin materials in hihly confined eometries ere the calorimetric studies of Jackson and McKenna 11. These studies involved oranic lass formin liquids confined to the pores of Vycor lass. The T values for the confined systems ere less than that of the bulk ith a maximum effect for o-terphenyl confined to 40 A pores here the T value as reduced 18 K belo the bulk value. More recent studies of lass formers confined in pore lass have involved dielectric spectroscopy 12. These studies have revealed faster dynamics in confined systems and have suested a lenth scale for lass transition dynamics of A. A complication, hich has been noted for usin pore lass as the confinin medium is the influence of the interfacial interaction. It has been found that the observed dynamics depend stronly on the treatment of the pore surface 13. Furthermore, once treated, it is difficult to quantify the interfacial properties. A second disadvantae of such studies is that the confinement dimension, hich may be probed, is limited by that of available pore lass hile the pore size distribution can be broad.

4 170 ( ) J.A. Forrest, K. Dalnoki-Veress Ad ances in Colloid and Interface Science An attractive sample choice for studies of finite size effects is that of thin polymer films. Foremost amon the advantaes of this sample eometry is that the confinin dimension, the film thickness, can be continuously varied over many orders of manitude from nanometers to micrometers. Furthermore, there are a lare number of polymers hich ill readily vitrify rather than crystallize, and this, combined ith many substrate materials and treatments, allos a rane of interfacial interactions to be investiated. Utilizin polymer film samples also allos for the preparation and study of free-standin films. We shall sho later that the ability to study free-standin films has provided many advances in the study of finite size effects in polymer film samples. The interfacial interaction beteen a polymer and substrate is also readily quantified by the use of contact anle measurements. Hoever, the use of polymeric materials introduces complications hich do not exist hen studyin other lass formers. Polymer molecules are extended objects ith a characteristic size, the r.m.s. end-to-end distance REE N 1 2, here N is the number of monomer units. This inherent lenth scale introduces the possibility of chain confinement effects as the film thickness h becomes smaller than the unperturbed molecular size. Such effects may be very difficult to distinuish as they can introduce anomalies in the dynamics ithout necessarily causin any chanes in the structural properties. One ay in hich it may be possible to identify chain confinement effects is that the manitude of such an effect, for constant film thickness, should depend on the molecular size. While the existence of chain confinement effects may obscure observation of finite size effects, they are interestin in their on riht as they serve as a probe of fundamental aspects of perturbations of polymer dynamics. 2. Measurin the lass transition in thin films As the temperature of a lass-formin material is loered, the relaxation times become very lare. A result of this is that certain types of motion ill be frozen out on the time scale of a particular experiment, and they no loner contribute to such quantitities as the thermal expansion or heat capacity. Since the relaxation times vary stronly ith temperature, there is an apparent discontinuity in these thermodynamic quantities. Thus, the kinetic lass transition appears experimentally to be quite similar to a second order thermodynamic phase transition. In bulk materials, T is either defined in terms of these near discontinuities, or alternatively, hen certain relaxation times are equal to a predefined value Ž usually 100 s.. All of these definitions of the lass transition lead to approximately the same measured T value. Since the measured T value depends on the thermal treatment of the sample, includin the heatin and or coolin rate durin the measurements, it is important to kno the measurement conditions hen makin comparisons beteen different experiments. For the case of thin polymer films, the most common measurement techniques are those that probe, directly or indirectly, the thermal expansion of the sample 14. Ellipsometry is the most common technique to measure T in supported

5 ( ) J.A. Forrest, K. Dalnoki-Veress Ad ances in Colloid and Interface Science polymer films, and has even recently been applied to free-standin films. Ellipsometry measures the ellipticity induced upon interaction ith Žeither reflection from or transmission throuh. a sample. For a simple isotropic polymer film, the measured quantities can be related in a straihtforard manner to the refractive index Ž n. and thickness Ž h. 15 of the thin film. Furthermore, small chanes in thickness and refractive index typical of most of the ellipsometry experiments, can be shon to be linearly related to small chanes in the ellipsometric measurables. Since both these quantities vary ith the density of the sample, they necessarily exhibit a kink at the lass transition temperature T. The inversion of ra ellipsometric data to obtain thickness and refractive index as a function of temperature has been carried out for the case of both supported 16,17 and free-standin 18 films. For both types of samples, the T obtained from the ra ellipsometric data as the same as that obtained from analysis of the thickness vs. temperature data. In practice, the relation beteen the physical quantities h and n, and the ellipsometric variables P and A, means that the inversion to h and n is rarely carried out. Ellipsometry has been shon to be capable of measurin T values in supported polymer films as thin as 50 A and free-standin films as thin as 200 A. The common method of determination of T is by selectin to linear reions of the data and findin the intersection point beteen the extrapolated lines. While this method is enerally satisfactory, it relies on an initial estimate of T, hich necessarily affects the results. To avoid this bias, an alternative method has recently been employed 18. In the lass transition reion, the thermal expansion coefficient varies from that of the lass to that of the melt over a very small temperature rane. This near discontinuity at the transition is ell described by a tanh-profile. By interatin this tanh profile one can derive the folloin expression for the film thickness, hich is also applicable for measurement of any quantity that varies linearly in the melt and lass reion ith temperature: ž / ž / ž / M G T T M G ht Ž. ln cosh Ž T T. c. Ž Here c is the value of the film thickness at T T, is the idth of the transition beteen the melt and the lass, and M and G are the dh dt slope values for the melt and lass, respectively. A value of T may be obtained by fittin ht Ž. to Eq. Ž 1.. The standard determination of T has 4 explicit parameters for the to linear reions, and additional 2 implicit parameters in the choice made for the beinnin and end of the transition reion. In addition to havin less free parameters, Eq. Ž. 1 avoids the ambiuity of the more standard method of determinin T. A second technique, hich has been successfully used to measure T in thin supported films, is that of X-ray reflectivity. This technique is also able to provide a sufficiently accurate measure of film thickness to allo measurements of T.A limitin factor in the utilization of reflectivity techniques vs. ellipsometric ones is the rate at hich data can be acquired. In a typical ellipsometric experiment, the

6 172 ( ) J.A. Forrest, K. Dalnoki-Veress Ad ances in Colloid and Interface Science data acquisition rate is sufficient that many data points can be required per deree hile rampin the temperature at rates as hih as 10 K min. In contrast, reflectivity techniques require the sample to be held at constant temperature for many minutes for each datapoint. Recently, a number of other techniques have been used to measure T in thin films. Such techniques include positron annihilation lifetime spectroscopy 19 Ž a technique also used in bulk polymers., optical aveuide spectroscopy 20, and capacitance measurements 21,22. For the case of free-standin films, there is a much more limited rane of techniques, hich have been utilized to measure the T value. Foremost amon these techniques is that of Brillouin liht scatterin Ž BLS By measurin the frequency shift of liht, hich is scattered from thermally excited film uided acoustic phonons, a sensitive probe of the material density is provided 26,27. BLS has been used successfully to measure T for free-standin polymer films ith thicknesses as small as 200 A. One unfortunate aspect of the BLS technique is that determination of a sinle T value can take as lon as 20 h. Recently, transmission ellipsometry has been used to measure T in free-standin films 18. Ellipsometry provides a much more rapid measurement, but suffers from a hiher sensitivity to sample defects such as rinkles, than does BLS. 3. The lass transition in supported polymer films 3.1. Measurements of the lass transition in supported films The first systematic investiation of T values in thin polymer films as per- formed by Keddie, Jones and Cory 16, and involved ellipsometric measurements of T in films of polystyrene Ž PS. supported on hydroen passivated SiŽ 111. afers. The film thickness, h, as varied from 3000 A don to 100 A. This studẙ revealed the remarkable observation that the T values for films ith h 400 A as reduced belo the bulk value. This reduction in T as found to increase as the film thickness as loered. The loest measured T value as 25 K less than the bulk value and as observed for a film thickness of 100 A. Films composed of 3 PS ith M values ranin from to Ž REE from 200 to 1000 A. ere studied in order to investiate the importance of polymer chain confinement. For all samples considered, the measured T values ere indepen- dent of M and the data ere collectively described by the empirical relation a bulk T T 1 Ž 2. h ž / here T bulk is the value of T for bulk PS. The best fit to the measured T values as provided by a 32 A and 1.8. This effect as suested as bein dominated by the existence of a liquid-like layer near the free surface ith a characteristic size hich increased as the temperature as raised and diverin at T.The intuitive idea of a surface layer ith hiher mobility is still incorporated

7 ( ) J.A. Forrest, K. Dalnoki-Veress Ad ances in Colloid and Interface Science into more recent attempts at modelin. Hoever, the idea of a lenth scale of mobility hich increases ith temperature is in contrast ith the temperature dependence predicted Ž and observed in simulations. for the lenth scale of cooperative motion. There is also no evidence for a lenth scale, hich diveres ith increasin temperature from other experiments or simulations. Kim et al. 28 have recently proposed an alternative parameterization of the data hich allos T data for thin films of many different polymers to be described ith only a sinle material-dependent fit parameter. In order to ain an understandin of the lass transition in more eneral terms, it is important that finite size effects in polymer films are not restricted to a sinle polymer material and, instead, exhibit some deree of universality. Recent measurements have confirmed that the T anomalies are not peculiar to the polymer PS. Usin the technique of optical aveuide spectroscopy, Prucker et al. 20 have shon that for PMMA films supported on hydrophobic lass substrates Žtreated ith HMDS., the measured T values decrease ith decreasin film thickness. In complete analoy to the data for PS, the T values for the PMMA thin films ere also found to be described by Eq. Ž. 2. For PMMA, the parameters ere a 3.5 A and , hich ere different from those for PS. The ability of the same functional form to describe the data for the to polymers is intriuin, but since Eq. Ž. 2 is purely empirical, it is not possible to ascribe physical meanin to either of the parameters. Finally, it is orth notin that very similar behavior in T vs. h has also been observed for thin polycarbonate films 17 as ell as films of polyž -methyl styrene. and polysufone 28 Since the initial investiations of Keddie et al., there have been many other studies for PS on a variety of different substrates, and employin a number of experimental techniques. Researchers usin ellipsometry 24, X-ray reflectivity 29, positron annihilation 19, and dielectric 22 techniques have all reached the same conclusion the T value of thin PS films is reduced belo the bulk value, and this effect becomes more pronounced for films ith smaller values of film thickness. The overhelmin consensus beteen the conclusions from these different studies is best demonstrated by Fi. 1, hich shos all measured T values presented in the literature for thin PS films supported on substrates. For reasons of clarity, e have not distinuished the results of different studies. A similar plot, hich does differentiate the different roups, but does not include the recent T data of reference 22, can be found in reference 30. While there is some scatter in the quantitative values, the qualitative trend mentioned above is completely obvious. This areement beteen a variety of techniques also serves to validate each of the techniques used. Despite the lare number of experimental studies of the T value in thin supported films, very fe ideas have been put forth reardin the oriin of the effect. The most likely reason for this is the scatter beteen the results from the different studies in Fi. 1, hich suests that the details of the interaction beteen the polymer and the substrate are important to et quantitative areement beteen different studies. This complication is removed in the studies of free-standin films, and it as exactly this fact that first motivated measurements of T in free-standin films.

8 174 ( ) J.A. Forrest, K. Dalnoki-Veress Ad ances in Colloid and Interface Science Fi. 1. Compilation of all measured T values for supported PS films. Measured values are from references 16,19,21,22,24,29,35. The importance of the polymer substrate interaction as reconized early and this has resulted in a number of studies aimed at directly studyin this effect. One such study as an extension of the ellipsometric studies of Keddie et al. to ultrathin films, hich ere physically rafted to the substrate 31. For such thin films, it may be arued that the polymer substrate interaction ill dominate the behavior, and it as observed that for sufficiently thin films the trend of T decreasin ith h is actually reversed, and for films ith 50 A h 100 A, the measured T values increase ith decreasin film thickness. A quantitative expla- nation for this observation has recently been suested 25. An alternative to studyin ultrathin films to focus on the effect of the polymer substrate interaction is to study systems here one expects a much stroner attractive interaction. One example of this is the study by van Zanten et al. for poly-2-vinylpyridine on oxide-coated Si substrates 32. In this system the measured T value as observed to increase above the bulk T, ith a maximum increase of 50 K for a 77-A film. Perhaps the most extensive body of data concernin the influence of the polymer substrate interaction on the measured T value is for polymethyl methacrylate

9 ( ) J.A. Forrest, K. Dalnoki-Veress Ad ances in Colloid and Interface Science Ž PMMA.. Keddie et al. shoed that the nature of this interaction could qualitatively chane the thickness dependence of the T value 33. For PMMA films on Au-coated lass substrates, the measured T value as found to decrease ith decreasin film thickness. For the same polymer on oxide-coated Si, the T value as found to increase above the bulk T for sufficiently thin films. Later studies by Grohens et al. 34 usin PMMA molecules ith different tacticity ere able to sho a direct correlation beteen the density of polymer substrate interaction ith the measured T value. While the T value of many polymers has been shon to be sensitive to the substrate used, it does not appear to be sensitive to the method of preparin the thin film. For the case of PS, Keddie et al. shoed that spincast films behaved quantitatively similar to rafted ones. For PMMA, Prucker et al. observed similar T reductions for films, hich ere spincast, rafted, or prepared usin the Lanmuir Blodett technique Resol in contro ersy in thin film T studies The discussion above demonstrates the importance of the strenth of interaction beteen the polymer and substrates on measured T values. In contrast, Fi. 1 clearly shos that for the case of PS, this interaction does not appear to dominate the behavior. This contradiction is most clearly illustrated in the idely discussed apparent discrepancy beteen the studies of Keddie, Jones and Cory 16, and a similar study on the same system usin X-ray reflectivity 35. The reflectivity study claimed that the T value for PS films on hydroen-passivated Si substrates as increased to a value at least 40 K reater than their measured bulk T for film thickness h 400 A. The contradiction ith the results of reference 16 as suested to be due to a stron sensitivity to sliht differences in the substrate properties. While this claim as not supported by any actual measured T values, hich increased for decreasin film thicknesses, the study continues to be idely cited as an important example of the extreme sensitivity of the T value to the substrate properties. As shon in Fi. 1, there is a lare body of experimental evidence hich demonstrates that for the case of PS films the T values are only eakly sensitive to the properties of the substrate. Given no that reference 35 stands out in contrast to many other studies, it is prudent to consider it in more detail. Fi. 2 reproduces the X-ray reflectivity data of reference 35. For the three thickest films, a T can be determined from the data by the kink in the thickness vs. temperature data. For the thinnest film shon in Fi. 2, Žand apparently for all films ith h 437 A. no break in the thickness vs. temperature data can be distinuished and the slope of the data is consistent ith a lassy value of the thermal expansion coefficient. This led to the inference that for films ith h 437 Å the T value had increased to a value reater than the maximum temperature considered in this case 430 K. The implication as that the T value increased from 390 K for h 497 A to a value reater than 430 K for h 437 A Žin these measurements bulk T bulk 390 K, i.e. 20 K reater than the typical value for PS.. While it is possible that the T value increases from the bulk value to one

10 176 ( ) J.A. Forrest, K. Dalnoki-Veress Ad ances in Colloid and Interface Science Fi. 2. Film thickness vs. temperature data from reference 35. The solid lines are the linear fits to the lass and melt temperature reions, hich ere used to measured the T values. at least 40 K hiher in such a small rane of thickness that intermediate T values cannot be observed, it does not seem likely. This is especially true iven the consensus of all of the measurements shon in Fi. 1. An alternative explanation for the data presented in reference 35 and reproduced in Fi. 2 has also been suested in references 24,30. The explanation allos all data to be explained in a simple unifyin frameork ith no resultin contradictions. Furthermore, this approach, usin the data of reference 35 hihlihts another anomalous property of thin PS films. An analysis of the slopes of the thickness vs. temperature data in Fi. 2 reveals that hile the thermal expansivity 1dh ž / in the lassy state is the same for all film thicknesses, the thermal h dt expansivity of the melt state varies ith film thickness; decreasin as the film thickness is loered. The most important consequence of this fact is that the contrast of the transition; the ratio of the melt expansivity to that of the lass is also a decreasin function of film thickness. As the contrast of the transition decreases, it becomes more and more difficult to identify the transition. For a contrast of 1 it is, by definition, not possible to identify a transition at all. In practice, any data ill exhibit some scatter, and identification of the lass transition becomes impossible for a contrast value somehat reater than unity. The decrease in contrast for decreasin film thickness is evident from Fi. 2, and is further quantified in Fi. 3.

11 ( ) J.A. Forrest, K. Dalnoki-Veress Ad ances in Colloid and Interface Science Fi. 3. Normalized lass transition contrast for thin PS film. The solid curves are the 1 h fits from references 17 Ž upper curve. and 26 Ž loer curve., and the data points are obtained from Fi. 2. The dashed curve is a 1 h fit to the contrast values found from Fi. 2. The plot in Fi. 3 explicitly shos the film thickness dependence of the thermal expansivity. The data points are measured values of the transition contrast, normalized so that different studies may be compared. In this plot a value of zero corresponds to no transition contrast Ži.e. the lass and melt expansivities are the same., and the shaded reion represents the rane of contrast for hich it is enerally not possible to identify the kink needed to measure T. Also shon on this raph is the film thickness dependence of the contrast for to additional studies 16,19, hich both shoed T values decreased belo the bulk value. These to solid curves are fits to a 1 h functional form, hich as used in both studies to parameterize the results, and can be shon to be consistent ith a multilayer model for the polymer film dynamics incorporatin a melt-like layer at the free surface. It is evident that all of these studies sho the same qualitative decrease in the contrast of the transition. A more detailed comparison reveals that there are systematic deviations beteen the studies, hich ill lead to different limitin values of the film thickness here a T can be observed. The dashed lines in this fiure correspond to a fit of the symbols to a 1 h film thickness dependence. This representation shos that hile the data of reference 35 does not support a T value, hich increases as the film thickness is loered, it certainly does support a decreasin contrast of the lass transition. In fact the extrapolation provided by the dashed line fit demonstrates that the reflectivity studies should not be able to determine a T for films ith h 400 A. The alternative explanation for the data in reference 35 is simply that the lass transition still occurs in the experimental temperature indo, but ith too lo a contrast to be identified. We reiterate that this decrease in contrast is observed in all studies of T in thin films and has been studied explicitly in references 16,19, and that this simple explanation, supported by other experimental studies, resolves the controversy associated ith this ork.

12 178 ( ) J.A. Forrest, K. Dalnoki-Veress Ad ances in Colloid and Interface Science While many studies have reported this decrease in the contrast of the transition, there is a remainin discrepancy in hich expansivity is dependent on film thickness. The data in reference 35 clearly shos that it is the expansivity in the melt hich varies ith film thickness, and this conclusion is supported by the PALS study of reference 19 as ell as by studies of free-standin films 36. The ellipsometric study of reference 16 suests instead that it is the expansivity of the lass, hich varies ith film thickness. This issue is currently unresolved, and more detailed study of thermal expansion in thin films is certainly arranted. Finally, e note that in BLS studies of the contrast of the lass transition in free-standin films, a much more complicated behavior as observed ith a contrast hich did not decrease monotonically in the same ay that Fi. 3 demonstrates for supported polymer films 36. A second area of controversy in the lass transition of thin films involves attempts to measure the dynamics more directly. A straihtforard ay to probe dynamics in thin films is to look at the diffusion of entire chains. Such studies have been performed and have found the somehat surprisin result that the diffusion of PS chains both in the plane of the film 37 as ell as normal to the film plane 38, are reduced for thin films compared to thick films or bulk samples. The reductions in chain diffusion occur for film thickness h 1000 A. The observation of sloer chain motion seems to disaree ith the idea of loer T values in thin films, hich ould suest an enhanced mobility. It should be noted, hoever, that the chanes in diffusion are observed for substantially thicker films than those exhibitin T reductions. Inferences about T from the dynamics of entire chains must be made ith care as hiher semental mobility is obviously a necessary condition for enhanced chain mobility, but it may not be a sufficient condition. For example, pinnin a small fraction of a polymer chain can lead to a case here the chain ill not be able to diffuse Ž leadin to a vanishin diffusion constant. even for very hih semental mobility. This example suests that a series of measurements at a sinle temperature and decreasin film thicknesses does not provide a quantity hich can be compared in a straihtforard manner ith measured T values. This may be stated more quantitatively if e recall that the chain diffusion ill be of a Voel Fulcher form ith DT Ž. D exp B Ž T T., here T Ž T 50 K We have already suested that the observed chanes in the thermal expansivity of the thin film melt, hich are observed for films ith h 1000 A, may be caused by certain types of motion not contributin to the thermal expansivity. It is obvious that the freezin out of any type of motion should result in sloer chain diffusion. The manifestation of this effect in chain diffusion studies ill be a film thickness dependence of D 0. This in turn leads to the observed sloer diffusion independent of any chanes in the T value of the film. We stress that in order to use chain diffusion studies to compare to the T value, it is the temperature dependence of the diffusion constant, hich must be measured. Such measurements have not yet been performed. Finally, e note that measurements in both free-standin and supported films have been performed to look at the semental dynamics, hich are expected to couple directly ith the T. In this case, complete areement has been

13 ( ) J.A. Forrest, K. Dalnoki-Veress Ad ances in Colloid and Interface Science found beteen measured semental dynamics and measured T is discussed in more detail belo. values 21,22,39 as 3.3. Other probes of dynamics in thin polymer films Measurements of the lass transition are an indirect probe of the dynamics in thin polymer films, and provide a sinle value to describe the entire temperaturedependent dynamics of the system bein measured. In addition to the measurements of hole chain diffusion discussed above, there have been a number of recent studies, hich focused on measurin the dynamics in thin polymer films. The suestion that reduced T values result from enhanced dynamics at the polymer free surface, has prompted studies aimed at directly measurin the relaxation properties of the polymer surface. The first direct measurements of relaxation dynamics in thin polymer films ere made by Hall et al. usin second harmonic eneration 40 to study probe-doped polymers. These studies revealed that for films ith decreasin film thickness, the relaxation functions became broader, but the averae relaxation time remained the same. These results ere noted to be consistent ith the small chanes in T observed for thin films of the polymer, polyž methyl methacrylate.. More direct comparisons ith the data in Fi. 1 can be made by considerin studies on relaxation in thin films of PS. Quartz crystal microbalance measurements of the adhesion of small particles to thin PS films, have been used to obtain a sinature of relaxation 39. The film thickness of this relaxation sinature as found to aree quantitatively ith the data in Fi. 1. Recent studies by Schab et al. 41 have measured the relaxation of birefrinence induced by rubbin thin films of PS. These studies revealed that for films less than 250 A, the relaxation as much faster than that for thicker films and corresponded to a decrease in the T value of K. Dielectric spectroscopy has also been employed to measure the relaxation function of thin PS films on Al-coated substrates 21,22. The relaxation functions obtained aree quantitatively ith the measured T values, but this areement appears to be a result of a substantial broadenin of the relaxation function rather than a simple shift to loer temperature. Further studies to directly probe relaxation functions in thin films should help to clarify these initially intriuin observations. Measurements of relaxation of the polymer surface offers tremendous promise as a direct probe of the proposed enhanced surface mobility used to explain T reductions in thin films. A variety of experimental techniques have been applied to this problem, but a clear experimental consensus has not yet emered. Positron annihilation techniques have been used to probe the near surface reion of PS films and has led to conclusions of both enhanced 42 as ell as bulk-like 43 surface dynamics. NEXAFS has been used to investiate the surface relaxation of rubbed films of PS 44. The relaxation of the dichroism induced by the rubbin procedure as monitored and not seen for temperatures less than the bulk value of T. Scannin force microscopy has also been used to probe the surface properties of polymer films throuh the measurements of friction forces 45. These studies

14 180 ( ) J.A. Forrest, K. Dalnoki-Veress Ad ances in Colloid and Interface Science have also suested an enhanced mobility at the polymer free surface for a number of different polymers includin PS. 4. The lass transition in free-standin films The controversy concernin the effect of the substrate in thin film T studies prompted studies of free-standin films. The first measurements of the T value in free-standin films ere the BLS studies of PS films ith thickness h beteen 200 and 2000 A 23. The results of this study ere remarkable in several aspects. The measured T values in the free-standin films exhibited reductions belo the bulk value, hich ere much reater in manitude than those reported for supported films; ith a 200-A film havin a T value reduced by 70 K belo the bulk value. For comparison, a supported film of the same thickness exhibits a T reduction of only 10 K. Consistent ith this larer manitude of T anomalies, as the fact that T reductions ere observed for much larer values of the film thickness; up to 700 A. Finally, the film thickness dependence of the T values in free-standin films as found to be qualitatively different from Eq. Ž. 2. The reduced T values ere accurately described as a linear function of film thickness. An extension of the BLS studies to a second value of M, revealed a stron M dependence of the T value 24, in contrast to the observations for supported films. The stron M dependence observed in these studies revealed the importance of chain confinement effects for hih M, free-standin films. These studies emphasized the importance of a detailed study of the M dependence of the T in free-standin PS films. This is necessary to characterize in more detail, the M dependence, that has been observed; and also to search for any finite size effects. The challene for more detailed studies of T in free-standin polymer films has been met by to different studies, each focusin on a different M reime. BLS studies have been used to measure the film thickness dependence of PS films ith M in order to explore the lo M reion 36. This study is joined ith transmission ellipsometry studies here the film thickness dependence of T values as studied for PS ith M The data from both of these separate studies are shon collectively in Fi. 4, hich is the free-standin film analo to Fi. 1. Comparin Fi. 4 ith Fi. 1, e notice the free-standin films exhibit a much richer behavior than their supported counterparts. Most notably, the effects on T are much larer than those for supported films. For values of M in the entire rane, T reductions as lare as 70 K are observed. More importantly, e notice a complicated M dependence for free-standin films, hich did not exist for supported films. As as first noted in reference 36, the data seem to naturally divide into to distinct reimes of M. For a value of M , the film thickness dependent T values do not appear to exhibit any discernable M dependence. In addition, the dependence of T on h is not linear. For M , the T values are a linear function of film thickness ith a threshold and slope, hich are dependent on M thouh this dependence appears to saturate for

15 ( ) J.A. Forrest, K. Dalnoki-Veress Ad ances in Colloid and Interface Science Fi. 4. Measured T values for free-standin polymer films. The solid symbols are obtained ith ellipsometry and taken from reference 18. The hollo symbols are obtained usin BLS, ith a vertical bar indicatin the data from reference 24 and a horizontal bar indicatin data from reference 36. very lare values of M. For the purposes of further discussion, e ill use the suestion provided by the data and divide the discussion into these to reimes of M. We note that there are no datasets exhibitin intermediate behavior T for free-standin films ith M As first noted in reference 24, the data for hih M displays some extraordi- nary characteristics. For any particular value of M, the measured T values appear to be a linear function of the film thickness. For film thicknesses don to a certain threshold value h 0, the T T bulk, and for h h 0, the T T bulk. The M dependence evident from Fi. 4 certainly shos that confinement of the polymer chains is an important factor in the T reductions, but the behavior is more complicated than one miht at first expect. The most straiht-forard explanation ould be that the T value shos anomalies from the bulk value for h R EE, and thus, e ould expect that h0 REE ould be constant. We miht also expect the slope of T Ž h. to vary in the same ay so that normalizin the film thickness by plottin h REE instead of simply h, e could collapse the data onto a sinle line. Unfortunately, such a simple scalin relation has been shon to be insufficient to describe the data 18. A recent study focused on the quantification of the M dependence in the hope that the mechanisms responsible for T reductions may be understood from the scalin dependence of T on h and M 18,46. The experi- mental details of this study are described by Dalnoki-Veress et al. 18 and here, e only present a brief overvie. In these studies, transmission ellipsometry on

16 182 ( ) J.A. Forrest, K. Dalnoki-Veress Ad ances in Colloid and Interface Science Ž 3 Fi. 5. Plot of T vs. h for the hih-m reime M The straiht solid lines are the best fit lines to the reduced T data and intersect at a common point Žh, T.. The solid curve represents the averae reduced T values for the lo-m reime. See the text for a discussion of the dashed lines labeled M, M and M. free-standin films as a function of temperature, provided a relatively quick and straiht-forard measure of T, makin the characterization of six molecular eihts ranin from to possible. The data for the hih M study are shon in Fi. 5. One of the most strikin aspects of the data is that the transition from the normal bulk lass transition to reduced T values as the thickness is decreased, appears to be very sharp. Despite considerable effort to measure in the transition reion, no deviation from to Ž bulk linear reions could be observed i.e. no curvature near T.. The sudden nature of this transition is consistent ith the existence of an alternative mechanism for mobility, hich is distinct from that of the bulk, but becomes more important in thin films. The mechanism responsible for lass transition in bulk materials bulk obviously results in T T Ž indicated by the dotted line in Fi. 5.. As the film thickness is decreased, deviations from bulk behavior ill be observed hen the thin film mechanism becomes a more efficient mechanism for mobility than the bulk mechanism. This competition beteen to distinct mechanisms as a consistent interpretation of the data as first discussed by de Gennes 47 and later in 46, and ould be expected to result in the sharp transition observed in the data. Examination of Fi. 5 reveals that the slope of the reduced T data as ell as the intersection h0 ith the bulk line at T bulk both increase monotonically ith increasin M. A surprisin aspect of the data is revealed by extendin the plot to

17 ( ) J.A. Forrest, K. Dalnoki-Veress Ad ances in Colloid and Interface Science hiher T and h; all the best fit lines to the reduced T data intersect at a sinle point Žh, T.. This is perhaps the most poerful suestion of the data, and clearly, reardless of the mechanism responsible for the anomalous reductions in T, determinin the physical sinificance of the point Žh, T. is crucial to developin an understandin of this mechanism. The intersection of these lines necessarily means that ŽT T. Žh h. and e rite Ž. Ž.Ž. Ž. T T M h h, 3 here all the M dependence is no in the slope parameter Ž M.. The intersec- tion of the best-fit lines to the reduced T data is iven by Žh, T. Ž nm, K.. The splittin Žthe temperature at hich the -relaxation mode, associated ith semental mobility, and the -relaxation, associated ith side roup relaxations, become distinct from each other. occurs at a temperature of T 423 K. Thouh possibly a coincidence, the fact that T T introduces the possibility that the mechanism for mobility resultin in reduced T values in thin films, may be related to the motion of the side roups. The simple analysis of the data presented in 18 and outlined here reveals that all the molecular eiht dependence of the anomalous T reductions is contained in the slope parameter Ž M.. As discussed above, Ž M. is not proportional to M 1 2, thus requirin another description of on M. An empirical approach leads to Fi. 6 here the slope parameter is plotted as a function of lož M.. The excellent areement of the data ith a straiht line in this plot makes it possible to parameterize the data as Ž. Ž. Ž. M bln M M ; 4 Ž. Ž. 3 here b K nm and M Without at least an intuitive reason for this functional form, this expression must be rearded as simply a convenient parameterization of the data and any expression that parameterizes the data accurately is equally valid. The extrapolation of the best fit line in Fi. 6 to Ž. 3 0 results in M This limit is illustrated by the dashed line labeled M in Fi. 5. M is obviously a loer limit for observin any effect due to the mechanism causin T reductions in thin films for any temperature up to T.A ay to quantify the limitin M behavior in a ay hich is more directly comparable to experimental data, is to consider the smallest value of M for hich T reductions can possibly be observed. The dashed line in Fi. 5 labeled by M results in no T reductions resultin from the thin film mechanism for any film. The slope of this line, 0.05 K A, can be compared to Fi. 6 to obtain a loer limit M In practice, the loer limit may be extended even further by makin comparison to T reductions observed in the lo M limit. Reductions in T for lo M free-standin films Ž discussed in more detail belo. have been attributed to a finite size effect due to an intrinsic lenth scale for co-operative dynamics 25. For some values of M, these to mechanisms resultin in T reductions must both exist. We recall that in the hih M reime, the bulk

18 184 ( ) J.A. Forrest, K. Dalnoki-Veress Ad ances in Colloid and Interface Science Fi. 6. Plot of the parameter representin the slope,, of the reductions in T ith h as a function of M. mechanism and chain confinement mechanism compete, resultin in a sharp crossover determined by a sitch of the most efficient mode for mobility. In an analoous ay, the competition beteen chain confinement at hih M and finite size effects at lo M, must also be determined by the most efficient mechanism and result in a crossover of behavior. Reductions resultin from finite size effects, rather than chain confinement effects, are observed for free-standin films ith thickness h 500 A. A fit to all the data in the lo M reime here the finite size effects dominate, is indicated as the solid curve in Fi. 5. The estimated crossover M, is illustrated by the dashed line labeled M beteen Žh,T ) and tanent to the lo M curve. From the slope of this line, 0.1 K A, and Fi. 6 the crossover M can be estimated to be M This is in excellent areement ith the study of the lo M reime discussed in 25,36 and outlined belo. To summarize, the experimental data indicate four important results. Ž. 1 The sudden transition from bulk behavior to the linear reductions in T, indicate a competition beteen to distinct mechanisms. Ž. 2 Intersection of the best-fit lines to the reduced T values at ( h, T. results in Eq. Ž 3.. Ž 3. The slope parameter Ž M. is iven empirically by Eq. Ž 4.. Ž 4. The crossover from the hih M to lo 3 M reime is estimated to occur at M Combinin Eqs. Ž. 3 and Ž. 4 results in a simple expression for the T reductions in terms of film thickness and molecular eiht dependence: Ž. Ž.Ž. Ž. T T bln M M h h. 5 Fi. 7 tests the scalin of this expression explicitly, and all the reduced T values for all thicknesses and molecular eihts in the hih M reime are very ell

19 ( ) J.A. Forrest, K. Dalnoki-Veress Ad ances in Colloid and Interface Science described by Eq. Ž. 5. Not only does this expression quantify the six M values studied ith only four parameters, but all the T reductions due to confinement effects in eneral, are expected to be described by this expression as ell Importance of annealin history A concern associated ith the sample preparation of hih M polymer chains is the annealin history of the sample. In order to properly characterize the effects of chain confinement, e should study samples here the chains have been annealed to establish an equilibrium distribution of chain conformation. This is expected to require annealin times on the order of the reptation Ž or terminal. time r. Measurements of the creep compliance of PS ith M reveal that the end of the plateau reion correspondin to the reptation time occurs at r s at a temperature of 388 K 48 Žthe annealin temperature of the samples of. 3.4 r r the hih M study. Since M, e can obtain for the various M values of this study to establish annealin times t. For the loest to M values, and , the relaxation times are 3 and 9 h, respectively, and the r annealin time t. We ould then conclude that these samples are sufficiently r annealed. Hoever, for hiher molecular eihts this is not true, and t.in r particular, the lonest chains of this study have r 4.5 years. Clearly, this timescale is not easily accessible to experiment. Simply raisin the annealin temperature is also not feasible since holes ill form in the films. While hole formation is an indication that the polymers are mobile, this should not be taken as an indication that r is on an experimental time frame. This is because hole Fi. 7. The scalin behavior of the expression derived in the text, relatin T in the hih-m reime to both M and h.