Dynamics of Block Copolymer Melts

The combination of careful chemical synthesis with NSE and SANS experiments sheds some light on the fast relaxation processes observed in the collective dynamics of block copolymers melts. The results reveal the existence of an important driving force acting on the junction points at and even well above the ODT. Modelling the surface forces by an expression for the surface tension, it was possible to describe the NSE spectra consistently. The experimental surface tension agrees reasonably well with the Helfand predictions, which are strictly valid only in the strong-segregation hmit. Beyond that, these data are a first example for NSE experiments on the interface dynamics in a bulk polymer system. 

The dynamics of block copolymers melts are as intriguing as their thermodynamics leading to complex linear viscoelastic behaviour and anisotropic diffusion processes. The non-linear viscoelastic behaviour is even richer, and the study of the effect of external fields (shear, electric. ..) on the alignment and orientation of ordered structures in block copolymer melts is still in its infancy. Furthermore, these fields can influence the thermodynamics of block copolymer melts, as recent work has shown that phase transition lines shift depending on the applied shear. The theoretical understanding of dynamic processes in block copolymer melts is much less advanced than that for thermodynamics, and promises to be a particularly active area of research in the coming years. 

A review of the thermodynamics of block copolymer melts prior to the discovery of complex phases was presented by Bates and Fredrickson (1990). Ryan and Hamley (1997) have recently reviewed the morphology of block copolymers containing a glassy component, in the melt and glassy states, and a discussion of complex phases is included. Fredrickson and Bates (1996) and Colby (1996) have reviewed the dynamics of block copolymer melts, of which the former is a par-... 

We conclude this section by drawing attention to various theories considering the dynamics of block copolymer melts rheology of these systems has been considered [340-342], single chain dynamics and selfdiffusion [343, 344], nu-cleation of the ordered phase [61], ordering kinetics [345,346], and dynamics of concentration fluctuations [347]. These topics are not under consideration here, just as other extensions of the theory random copolymer melts [348, 349], multiblock copolymer melts [350] etc. 

The interest in the phase behaviour of block copolymer melts stems from microphase separation of polymers that leads to nanoscale ordered morphologies. This subject has been reviewed extensively [1 ]. The identification of the structure of bicontinuous phases has only recently been confirmed, and this together with major advances in the theoretical understanding of block copolymers, means that the most up-to-date reviews should be consulted [1,3]. The dynamics of block copolymer melts, in particular rheological behaviour and studies of chain diffusion via light scattering and NMR techniques have also been the focus of several reviews [1,5,6]. 

Fraai]e J G E M 1993 Dynamic density functional theory for micro-phase separation kinetics of block copolymer melts J. Chem. Phys. 99 9202... 

NMR has not been widely employed to study dynamics in block copolymer melts, although field gradient NMR can provide a wealth of information on the diffusion of block copolymer chains (Fleischer et al. 1993). The orientation of a deuterated homopolymer in a lamellar diblock copolymer (in a glassy state) was determined using 2H NMR by Valic et al. (1994,1995). Other applications of NMR to probe polymer chain dynamics and details of experimental protocols are described by Bovey and Jelinksi (1989). 

In this chapter we focus on melts of well-defined block copolymers synthesized anionically. i.e. block copolymers with a narrow molecular weight distribution. These polymers serve as model materials for investigating the rich phase behaviour and dynamics of block copolymers in the bulk and in thin films. 

Our understanding of the physics of block copolymers is increasing rapidly. It therefore seemed to me to be timely to summarize developments in this burgeoning field. Furthermore, there have been no previous monographs on the subject, and some aspects have not even been reviewed. The present volume is the result of my efforts to capture the Zeitgeist of the subject and is concerned with experiments and theory on the thermodynamics and dynamics of block copolymers in melt, solution, and solid states and in polymer blends. The synthesis and applications of these fascinating materials are not considered here. 

This chapter deals almost exclusively with neat, or pure, diblock copolymer melts. Polymer blends are discussed in Chapter 9, micellar solutions in Chapter 12, and stabilized suspensions in Chapter 6. In the following, Section 13.2 briefly reviews the thermodynamics of block copolymers, and Section 13.3 describes the rheological properties and flow alignment of lamellae, cylinders, and sphere-forming mesophases of block copolymers. More thorough reviews of the thermodynamics and dynamics of block copolymers in the liquid state have been written by Bates and Fredrickson (1990 Fredrickson and Bates 1996). The processing of block copolymers and mechanical properties of the solid-state structures formed by them are covered in Folkes (1985). Biological applications are discussed in Alexandridis (1996). 

Fraaije, J.G.E.M., Van Vlimmeren, B.A.C., Maurits, N.M., Postma, M., Evers, O.A., Hoffmann, C., Altevogt, P., Goldbeck-Wood, G. The dynamic mean-field density functional method and its application to the mesoscopic dynamics of quenched block copolymer melts. J. Chem. Phys. 106 (1997) 4260-4269. 

The impenetrability of assemblies of tethered chains has broad implications. Some of these are discussed in more detail in the sections on interactions, on dynamics and on block copolymer melts. Examples of phenomena that have been... 

The mean-field SCFT neglects the fluctuation effects [131], which are considerably strong in the block copolymer melt near the order-disorder transition [132] (ODT). The fluctuation of the order parameter field can be included in the phase-diagram calculation as the one-loop corrections to the free-energy [37,128,133], or studied within the SCFT by analyzing stability of the ordered phases to anisotropic fluctuations [129]. The real space SCFT can also applied for a confined geometry systems [134], their dynamic development allows to study the phase-ordering kinetics [135]. 

These concentration fluctuations are pivotal to the phase transitions in block copolymer melts and are dynamic in nature. They lead to a renormahzation of the relevant interaction parameters and are thought to be responsible for the induction of the first-order nature of the phase transition [264,265]. Such fluctuations are better studied in dynamic experiments. Thus, one can observe an increasing interest in diblock copolymer dynamics. These dynamic properties are being analysed through experimental, theoretical [266,267] and computer simulation approaches [268,269] with the aim of determining the main featirres of diblock copolymer dynamics in comparison to homopolymer dynamics. There are three main issues ... 

Block copolymers are widely used industrially. In the solid and rubbery states they are used as thermoplastic elastomers, with applications such as impact modification, compatibilization and pressure-sensitive adhesion. In solution, their surfactant properties are exploited in foams, oil additives, solubilizers, thickeners and dispersion agents to name a few. Particularly useful reviews of applications of block copolymers in the solid state are contained in the two books edited by Goodman (1982,1985) and the review article by Riess etal. (1985). The applications of block copolymers in solution have been summarized by Schmolka (1991) and Nace (1996). This book is concerned with the physics underlying the practical applications of block copolymers. Both structural and dynamical properties are considered for melts, solids, dilute solutions and concentrated solutions. The book is organized such that each of these states is considered in a separate chapter. 

The fascinating thermodynamics of block copolymers that results from microphase separation are the subject of the parts 2.2,2.3, and 2.4 of Chapter 2. Part 2.4 is concerned with the complex kinetic processes that accompany phase transitions, and the dynamic processes controlled by the structure of the block copolymer melt. 

The kinetics of ordering in block copolymer melts have been studied using cell dynamics simulations of the TDGL equation (Bahiana and Oono 1990 Chakrabarti et al. 1991 Puri and Oono 1988 Qi and Wang 1996, 1997 Shiwa et al. 1996). Here, the time evolution of the order parameter ip is followed ... 

Dynamic light scattering has traditionally been applied to polymer solutions, and DLS results for block copolymer solutions are discussed in Chapters 3 and 4. A number of recent papers have described the application of the technique to disordered block copolymer melts (Anastasiadis et al. 1993a,6 Boudenne et al. 1996 Floudas et al. 1995 Fytas et al. 1993 Jian et al. 1994a Stepanek and Lodge 1996 Vogt et al. 1994). Due to the limited range of dynamic time-scales that can... 

The dynamic structure factor of block copolymer liquids (melts and solutions) has been accounted for using dynamical mean-field theory by Benmouna et al. (1987a,6). For a block copolymer melt, the dynamic structure factor can be written (Stepanek and Lodge 1996)... 

Of particular importance are in situ SFM measurements, which allow real-time data collection during structure evolution [111, 112, 117, 133-135], Both concentrated block copolymer solutions [117, 136, 137] and block copolymer melts [111, 112] have been imaged in situ to access the microdomain dynamics. Figure 3... 

We will briefly discuss the molecular dynamics results obtained for two systems—protein-like and random-block copolymer melts— described by a Yukawa-type potential with (i) attractive A-A interactions (saa < 0, bb = sab = 0) and with (ii) short-range repulsive interactions between unlike units (sab > 0, aa = bb = 0). The mixtures contain a large number of different components, i.e., different chemical sequences. Each system is in a randomly mixing state at the athermal condition (eap = 0). As the attractive (repulsive) interactions increase, i.e., the temperature decreases, the systems relax to new equilibrium morphologies. 

Rheometers are currently under development that will enable the anisotropic stress tensor of anisotropic complex fluids such as block copolymer melts and solutions to be probed, even during large amplitude shear. Here, a small amplitude probe waveform is applied orthogonal to the primary large amplitude shear flow. This could provide the linear dynamic modulus of an anisotropic system under nonlinear flow. 

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