Microphase separation temperature

For most BC the phase diagram is characterized by the presence of an upper critical solution temperature, UCST, also known as an order-disorder transition temperature or a microphase separation temperature. Below UCST the block copolymers phase separate, while above it, an isotropic melt is obtained. Owing to the chemical... 

Fig. 15. Reciprocal of the peak intensity obtained from SAXS measurement of styrene/butadiene diblock copolymer plotted against the reciprocal of temperature T. Linear extrapolation of high temperature data to zero gives the spinodal temperature, while the first deviation of the observed intensity from the straight line gives the microphase separation temperature. (From Zin and Roe...

In the Gaussian thread limit analytic results have been derived for copolymer fluids using the molecular closures. " The analytic results provide insights to several key questions and behaviors that emerge from the numerical PRISM studies. These Include (1) the role of nonzero monomer hard-core diameter, density fluctuations, and concentration fluctuations on dlblock liquid-phase behavior and structure (2) relationship between phenomenological field-theoretic approachesand the molecular closure-based versions of PRISM theory and (3) the influence of molecular weight, composition, solution density, and chemical and conformational asymmetries of the blocks on copolymer microphase separation temperatures. 

In analogy with the conformationally and interaction asymmetric thread blend analysis discussed in Section VI.C, Schweizer has derived analytic results for the microphase spinodal based on the R-MMSA and R-MPY/ HTA closures. The focus here is not on the rather universal fluctuation stabilization phenomenon discussed above but the influence of system-specific block stiffness and attractive interaction differences on the location of the (spinodal) microphase separation temperature. 

Figure 2 Temperature dependent characteristic parameters ofP(S-b-B) during an upward and downward temperature scan, inverse of the normalized scattering peak maximum, I o/l (i o is the peak intensity at the transition), maximum position, q, and peak width, Aq, as obtained from fits of a Lorentz function to the q dependent scattering intensity. The solid lines are guides to the eyes. The data point in brackets represents the peak intensity of the sample directly q/ter the preparation. The dotted line indicates the position of the microphase separation temperature Tmst-...

The mean-field theory of Leibler agrees very well with experimental observations based on X-ray and neutron scattering when obtained relatively far from the microphase separation temperature (MST). In the vicinity of the MST, however, mean-field treatment is less accurate. Both, Leibler and Fredrickson and Helfand noted that the effective Hamiltonian appropriate for diblock copolymers is in the Brazovskii-universality class [15,16]. Based on the Hartree treatment used in the Brazovskii theory, Fredrickson and HeUand found that the structure factor can still be written as the mean-field expression Eq. (7.101), but with renormalized values % and N [16]. The fluctuation renormalization makes the order parameter nonlinear in x, and thereby nonlinear in T". This is shown in the experimental example given in Figure 7.13. 

We calculated the microphases of a thin film of neat three-block polystyrene - polybutadiene - polystyrene (SBS) deposited on a solid substrate [33]. The parametrization protocol was somewhat different from the case of L64, now using data on the microphase-separation temperature of a bulk melt to determine the critical Flory-Huggins value, rather than solution data. 

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