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The phase behavior of polydisperse multiblock copolymer melts : (a theoretical study)

(1998) Angerman, Hindrik Jan

Summary
The main theme of this thesis is the influence of polydispersity on the phase behavior of copolymer melts. With “polydispersity” we do not only refer to polydispersity in overall chain length, but also to polydispersity in the composition and the monomer sequence of the chains.
Study of the influence of polydispersity is important because synthesizing purely monodisperse copolymers is very difficult, and for most polymerization techniques the occurrence of a certain degree of polydispersity is inevitable. We start with a short discussion about phase separation.
A homopolymer is a chain molecule consisting of only one sort of link (monomer). For many homopolymer blends, i.e. mixtures of different homopolymers, the homogeneous state becomes unstable on lowering the temperature, and the different molecule species tend to separate from each other. The result is a splitting of the system into coexisting phases. Each of these phases separately is homogeneous, but they differ in composition. The separation of a polymer blend into coexisting homogeneous phases is called macrophase separation.
In a copolymer, on the other hand, different monomer types are chemically linked together.
Therefore, a complete separation of the system into the different monomer types is impossible.
Instead, on lowering the temperature the phase separation occurs on a microscopic length scale. Small domains rich in one monomer type are alternated by small domains rich in the other.
Usually, these domains are arranged in a regular pattern. When in a copolymer system such domains arise, we talk about microphase separation.
The research described in this thesis was restricted to copolymers consisting of two monomer types, henceforth denoted by A and B. Most attention was paid to the so-called random copolymers. In random copolymer chains, the correlation in chemical identity between two monomers decays exponentially with their mutual distance along the chain. It has been assumed that within the chains, like monomers tend to aggregate to form long sequences of identical monomers. Such sequences are called blocks. The block length distribution in random copolymers is very broad: the variation in the block lengths is of the same order of magnitude as the block lengths themselves. Homopolymers having such a length distribution can be formed by a polycondensation reaction, after which they can be linked together to form a multiblock copolymer chain.
With the phase behavior of a polymer system we mean the phase of the system as a function of temperature. The phase contains information about the volumes and compositions of the coexisting phases in case of macrophase separation, and the size and the spatial arrangement of the microscopic domains in case of microphase separation. In chapter 1 we describe the theory which enables the calculation of the phase behavior of a large class of polydisperse copolymer melts. In chapter 2 we describe how the regular periodic spatial arrangement of the domains in a microphase separated copolymer melt can be described mathematically. In chapter 3 the phase behavior of the correlated random copolymer melt is calculated in the so-called meanfield approximation, which means that it is assumed that the concentration profile is static (the concentration profile describes the spatial dependence of the A-monomer fraction). This approximation becomes more accurate if the block lengths in the system increase. In chapter 3 we derive an expression for the free energy of a random copolymer melt, and using this
expression it is shown that the system tends to microphase separate. The A-rich and B-rich domains appear to have a regular spatial arrangement despite the intrinsic disorder present in the sequence distribution along the chains.
In chapter 4 the study of the correlated random copolymer is continued by taking into account the possibility of macrophase separation. It is shown that for certain values of the composition and temperature the melt can indeed separate into coexisting phases, but at least one of these phases has to be microphase separated. Nevertheless, it is very doubtful whether the system will ever reach this two-phase state under experimental conditions, because macrophase separation requires a complete spatial rearrangement of the molecules, which is a very slow process due to the restricted mobility of the chains.
In chapter 5 we go beyond the mean-field approximation. As indicated above, in the mean-field approximation it is assumed that the profile is regular, smooth, and static. In reality, however, irregular, time-dependent disturbances are present. These disturbances are called fluctuations.
It is to be expected that due to the intrinsic disorder in the monomer distribution along random copolymer chains, fluctuations will be rather important in systems consisting of these molecules. This expectation is confirmed by the analysis in chapter 5. It is shown that the regular structures predicted in chapter 3 are strongly distorted, giving the concentration profile a disordered appearance.
In chapter 6 a more general class of copolymers is considered, namely polydisperse multiblock copolymers for which the average number of blocks per chain, and the average number of momomers per block are very large. The length distribution of the A-blocks is arbitrary, and may differ from the arbitrary length distribution of the B-blocks. The correlated random copolymer studied in the previous chapter belongs to this general class, if we choose a Flory distribution both for the lengths of the A-blocks, and for the lengths of the B-blocks.
In chapter 6 we calculate and compare the mean-field phase diagrams for various realizations of the block length distributions. By changing continuously the degree of polydispersity, it is possible to study its influence on the phase behavior.