Article pubs.acs.org/Macromolecules
Viscoelastic and Glass Transition Properties of Ultrathin Polystyrene Films by Dewetting from Liquid Glycerol Jinhua Wang and Gregory B. McKenna* Department of Chemical Engineering, Texas Tech University, Lubbock, Texas 79409-3121, United States ABSTRACT: We have used the liquid dewetting method originally proposed by Bodiguel and Fretigny (Eur. Phys. J. E: Soft Matter Biol. Phys. 2006, 19(2), 185−193) to study thickness effects (ranging from 4 to 154 nm) on the viscoelastic and glass transition behaviors of ultrathin polystyrene (PS) films. PS with molecular weights of 278 and 984 kg/mol and various thermal treatments were examined. Both glass transition temperature (Tg) reduction and film stiffening in the rubbery plateau regime were observed in the PS films as film thickness decreased. The value of the plateau compliance was found to vary approximately linearly on the log plot with the film thickness. No molecular weight effect was found for the dewetting behaviors of the PS films prior to the terminal flow regime, where the majority of the current work was carried out. The present results show that the film dewetting process for the polystyrene/glycerol couple has to be described as a “non-isothermal” experiment due to the changing glass transition as the film thickens. A numerical method is proposed to correct the experimental data to the “isothermal” and constant thickness condition. Interestingly, even though in the dewetting experiment the polymer thin films were exposed to the liquid glycerol, which was originally thought to be a condition similar to that of freely standing films, the film thickness dependence of the Tg is, in fact, similar to but weaker than, what is observed for PS thin films supported on SiO2 substrates.
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INTRODUCTION Upon confining materials to the nanometer size scale, one frequently observes changes in the physical properties.1−9 For crystalline materials, the melting point is known to decrease with decreasing crystal size and this can at least be qualitatively understood in terms of the surface to volume ratio through, e.g., the Gibbs−Thomson relationship or modifications thereof.10−12 For amorphous materials, the glass transition temperature (Tg) is one essential parameter used to characterize their properties. Jackson and McKenna first recognized the importance of size effects on the glass transition temperature of organic glass forming liquids in nanoporous confinement.13 And Keddie et al.2 were the first to observe a reduced glass transition temperature in thin polymer (polystyrene) films. The behavior of glass forming systems under confinement remains an area of intense investigation. It has been reported that molecular weight, 6,14−16 surface and interface interactions,1,6,17−19 annealing conditions20−23and experimental methods5,23−25 all have either positive or negative influences on the glass transition temperature of numerous amorphous materials especially thin polymer films. As summarized in a recent conference summary paper by one of the present authors,26 current literature reported results show obvious disagreement among different groups and different experimental methods. While there is no universal agreement for the size effects on the Tg and, consequently no general view of possible causes of, e.g., Tg reductions, it remains a challenge to bring together the apparently disparate results in a common explanation. Thus, the importance of system size for the thermoviscoelastic © 2013 American Chemical Society
response, including the glass transition behavior, of amorphous materials remains an unresolved problem. Recently, an attempt to resolve part of this problem was made by Bodiguel and Fretigny in a highly novel experiment in which polystyrene films were floated onto hot glycerol and allowed to dewet spontaneously.23 The experiment is conceptually a creep experiment in either biaxial compression or uniaxial extension and can be analyzed to give the creep compliance of the film as a function of time. Furthermore, because the glycerol is a liquid, there are two possible advantages to this test method over other methods. First, it was anticipated that the highly mobile glycerol surface would act in a fashion similar to the air interface seen by freely standing films, hence, it would provide an alternative to the “pseudo-thermodynamic” measurements11 of freely standing film properties. It provides a novel method to investigate the effects of thickness on thin film dynamics in a direct measurement of the creep compliance as a function of time and temperature. Though the method seems not to probe freely standing films, as found by Bodiguel and Fretigny,27 it does provide a direct mechanical probe of the film dynamics. Further, in examining thicknesses down to 20 nm, Bodiguel and Fretigny reported only weak changes in the glass transition temperature reminiscent of the changes in supported ultrathin films.27 Received: January 7, 2013 Revised: March 6, 2013 Published: March 15, 2013 2485
dx.doi.org/10.1021/ma400040j | Macromolecules 2013, 46, 2485−2495
Macromolecules
Article
S is positive, the film spreads and wets the substrate surface, while the film dewets when the parameter S is negative.23,27 In the present work, the spreading parameter for PS on glycerol is approximately −5 mN/m;27 thus, the PS films tend to shrink on the glycerol surface under the stress (σ(t) = S/h(t)).23 The strain response of the PS thin films can be obtained by analyzing the film area change with time (as measured in the experiment)using the Hencky strain equation23,27
The second advantage of the method is that, unlike the case of supported films, any solvent that might accumulate at the interface with the rigid substrate would not be expected to remain trapped here and would diffuse into the liquid (glycerol) substrate. As a result, issues of residual solvent, such as those raised by Kremer and co-workers20,21 should be minimized. One other aspect of ultrathin films that is relevant to the present paper are the observations from this lab24,28−30 that the rubbery plateau regime of ultrathin films inflated in both biaxial inflation of circular membranes and an extensional geometry using rectangular membranes shows dramatic stiffening in poly(vinyl acetate), polystyrene (PS), polycarbonate (PC) and poly(n-butyl methacrylate) (PBMA). This stiffening was not observed in the glycerol dewetting experiments of Bodiguel and Fretigny.22,27 The purpose of the present work is to examine the behaviors of ultrathin polystyrene films in the glycerol dewetting experiment developed originally by Bodiguel and Fretigny23 and to expand their work to thinner films of polystyrene. As we show subsequently, in these experiments, we reproduce the results of Bodiguel and Fretigny,23,27 but find that Tg does decrease when the film thickness is below the 20 nm thickness that they achieved and, similar to their findings, the results do not follow the behaviors observed for freely standing films, but look more like films confined to rigid substrates. We further find that an enhanced rubbery plateau stiffening of polystyrene observed in the nanobubble inflation experiment is also observed in the thin film dewetting experiments, but the film thickness dependence in the former instance is much greater following a power law of approximately 2 with thickness,28 while the dewetting experiments seem to be better described by a power law index near to unity, i.e., a linear dependence on film thickness. Finally, we show that the very rapid changes that occur in Tg when film thickness decreases below approximately 20 nm give an unusual result. Because the thickening in the films as they dewet from glycerol can be substantial (multiple nanometers), the Tg changes rapidly during the experiment and the film dewetting process is consequently like a nonisothermal experiment. Although many studies have been done to predict the thermomechanical behavior of glassy materials under nonisothermal conditions by analysis of the isothermal experimental data, less work has been carried out to obtain the isothermal response from nonisothermal experiments. In the present work, we propose a method to correct the thin film experimental data to the “isothermal” and constant thickness condition. In the next sections we describe the thin film dewetting experiment and its analysis, show our methods and report our results. We end with a discussion and a set of conclusions. Thin Film Dewetting: Theoretical Analysis. When a polymer thin film spreads on a solid or liquid surface, the dewetting phenomenon is initiated and driven by the minimization of system free energy (G).31 At constant temperature (T) and pressure (P), the change of total free energy per unit area (A) is referred to as the spreading parameter (S) and can be expressed as,32 S=−
dG = γl − γpl − γp dA
ε(t ) = H(t ) ln
A0 A (t )
(2)
where A0 is the initial film area and A(t) is the film area at time t, H(t) is the Heaviside function. Because volume conservation is valid during the experiment,23 A0/A(t) = h(t)/h0 and the instantaneous strain (ε(t)) can be directly related to the instantaneous film thickness (h(t)) ε(t ) = H(t ) ln
h(t ) h0
(3)
h(t ) = H(t )h0 exp(ε(t ))
(4)
And the instantaneous stress (σ(t) = S/h(t)) and σ0 = S/h0, thus σ(t ) = H(t )σ0 exp( −ε(t ))
(5)
In the dewetting experiment, the film thickness changes with time as the film shrinks. This changes the instantaneous stress value. In general, creep experiments under varying stress are analyzed using the principle of Boltzmann superposition to relate the strain and stress histories,33 t
ε(t ) =
∫−∞ D(t − t′) dσd(tt′′) dt′
(6)
where ε is the strain, σ is stress, and D is the creep compliance. Upon substituting eq 5 in eq 6, we obtain ⎡ ε(t ) = σ0⎢D(t ) − ⎣
∫0
t
D(t − t ′)
⎤ dε(t ′) exp( −ε(t )) dt ′⎥ ⎦ dt ′ (7)
Here, a concept “corrected strain (ε′(t) = σ0D(t))” is introduced, similar to Bodiguel and Fretigny’s work.27 Then, eq 7 can be rearranged as ε′(t ) = ε(t ) + σ0
∫0
t
D(t − t ′)
dε(t ′) exp(−ε(t )) dt ′ dt ′ (8)
Equation 9 is the numerical equation used to calculate the corrected strain.23,27 ε′(ti) = ε(ti) +
∑ 0
