Dynamics in block copolymer solutions

Here D() is the infinite dilution diffusion coefficient, kd is the concentration coefficient and c is the concentration. A plot illustrating this behaviour is shown in Fig. 3.32. The concentration coefficient is given by (Vink 1985). 

The value of kA is large and positive for high molecular weight polymers in good solvents, where the term involving A2 dominates, while in theta solvents (A2 = 0), kd has a small negative value which reflects k, (Kent et al. 1994). 

There is a substantial body of work using dynamic light scattering to probe the hydrodynamic properties of poly(oxyethylene)-based block copolymers in aqueous solution. The work of Brown and co-workers has been reviewed by 

Chu and co-workers have also made extensive use of dynamic light scattering to study micellization in PEO/PPO triblocks. This work is discussed in Section 3.3.2 and reviewed by Chu and Zhou (1996), and we do not repeat details here. In addition, temperature-dependent micellization in solutions of a PS-poly (ferf-butylstyrene) (PlBS) diblock and PtBS-PS-PtBS triblock in dimethylac-etamide has been probed using this technique by Chu and co-workers (Zhou et al. 1993, 1995). Booth and co-workers use DLS routinely in their studies of PEO-PBO copolymers, as also discussed in Section 3.3.2 and reviewed by Booth et al. (1997). 

Field gradient NMR has been employed to determine the self-diffusion coefficient of a Pluronic triblock, and the hydrodynamic radius has been compared to DLS measurements on the same system (Almgren et al. 1992). NMR was found to give a somewhat lower value for the hydrodynamic radius than DLS. However, at infinite dilution the values obtained from the two techniques are the same. A similar observation has been made for eye I o - PB027P H 0,44 in aqueous solution (Yu et al. 1996c). Tin s effect has been attributed (Almgren et al. 1995) to the difference in dynamic averaging for the DLS and NMR experiments. In DLS, 

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This chapter is organized as follows. The thermodynamics of the critical micelle concentration are considered in Section 3.2. Section 3.3 is concerned with a summary of experiments characterizing micellization in block copolymers, and tables are used to provide a summary of some of the studies from the vast literature. Theories for dilute block copolymer solutions are described in Section 3.4, including both scaling models and mean field theories. Computer simulations of block copolymer micelles are discussed in Section 3.5. Micellization of ionic block copolymers is described in Section 3.6. Several methods for the study of dynamics in block copolymer solutions are sketched in Section 3.7. Finally, Section 3.8 is concerned with adsorption of block copolymers at the liquid interface. 

This chapter is concerned with experiments and theory for semidilute and concentrated block copolymer solutions.The focus is on the thermodynamics, i.e. the phase behaviour of both micellar solutions and non-micellar (e.g. swollen lamellar) phases. The chapter is organized very simply Section 4.2 contains a general account of gelation in block copolymer solutions. Section 4.3 is concerned with the solution phase behaviour of poly(oxyethylene)-containing diblocks and tri-blocks. The phase behaviour of styrenic block copolymers in selective solvents is discussed in Section 4.4. Section 4.5 is then concerned with theories for ordered block copolymer solutions, including both non-micellar phases in semidilute solutions and micellar gels. There has been little work on the dynamics of semidilute and concentrated block copolymer solutions, and this is reflected by the limited discussion of this subject in this chapter. 

Figure 67 shows Q QVQ2 vs. Q for both systems. As expected from Eqs. (142) and (143) their behavior is completely different. One can see that a pronounced divergency occurs at small Q-values in the semi-dilute block copolymer solution. If Qi(Q)/Q2 is analyzed in terms of a generalized mobility ji(Q) [see Eq. (94)], Fig. 68 results from the different concentrations of the diblock copolymer solution. Q(Q) varies both with Q and with c. In particular, the Q-dependence is indicative of the non-local character of the mobility and incompatible with the assumption of a pure Rouse type of dynamics. The... 

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... 

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. 

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... 

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). 

AZU Azuma, T., Tyagi, O.S., and Nose, T., Static and dynamic properties of block-copolymer solution in poor solvent I, Polym. J., 32, 151, 2000. 

Using this difference in transition temperatures, a dynamic unimer-micelle transition under the conditions of the BZ reaction was demonstrated. By adding the BZ substrates (HNO3, NaBr03, andMA) into the block copolymer solution, the oscillating behavior of the block copolymer under the constant conditions was analyzed. The scattering intensity and... 

Concerning the dynamics of block copolymers in solution, we have to consider on the one... 

Without exception, in all practical applications of block copolymers and block copolymer solutions, the mesoscale pattern determines the performance. And also, in almost all of these systems the dynamical pathway of formation is of... 

Waton, G., Michels, B., Zana, R. Dynamics of block copolymer micelles in aqueous solution. Macromolecules 2001, 34(4), 907-910. 

Fig. 6. Snapshot from a dynamic density functional simulation of the self-organisation of the block copolymer PL64 (containing 30 propylene oxide rmd 26 ethylene oxide units (EO)i3(PO)3o(EO)i3) in 70% aqueous solution. The simulation was carried out during 6250 time steps on a 64 x 64 x 64 grid (courtesy of B.A.C. van Vlimmeren and J.G.E.M. Praaije, Groningen).

The paper is organized in the following way In Section 2, the principles of quasi-elastic neutron scattering are introduced, and the method of NSE is shortly outlined. Section 3 deals with the polymer dynamics in dense environments, addressing in particular the influence and origin of entanglements. In Section 4, polymer networks are treated. Section 5 reports on the dynamics of linear homo- and block copolymers, of cyclic and star-shaped polymers in dilute and semi-dilute solutions, respectively. Finally, Section 6 summarizes the conclusions and gives an outlook. 

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