Polymer Solutions and Mixtures

In this paper, we have reviewed some recent applications of the HPTMC method. We have attempted to demonstrate its versatility and usefulness with examples for Lennard-Jones fluids, asymmetric electrolytes, homopolymer solutions and blends, block copolymer and random copolymer solutions, semiflexible polymer solutions, and mixtures. For these systems, the proposed method can be orders of magnitude more efficient than traditional grand canonical or Gibbs ensemble simulation techniques. More importantly, the new method is remarkably simple and can be incorporated into existing simulation codes with minor modifications. We expect it to find widespread use in the simulation of complex, many-molecule systems. 

In principle, this ratio can also affect the IP concentration profile in a quahta-tive sense. When considering a homogeneous epoxy-amine mixture just brought into contact with the surface of an adherend or a fiUer particle, preferential adsorption of the amine molecules will result in local variations of the amine/epoxy concentration ratio r (to be defined below). Assuming a comparably fast diffusion of the amine molecules, their quick enrichment at the interface will result in a near-interface zone of increased r values and an adjacent zone of amine depletion, i.e., with reduced r values. Similar concentration variations are dealt with in the field of surface-driven phase separation in polymer solutions and mixtures [8]. While the wetting layer is in local equihbrium with the depletion layer, the diffusion from the bulk down the concentration gradient into the latter feeds the growth of the former. 

Research on the spinodal decomposition of polymer solutions and mixtures began in relatively recent years, but a considerable body of experimental data has already been accumulated by several groups of workers. Major findings have been reviewed by Hashimoto [ 19, 20] and Nose [21], along with a relevant summary of the related theories. In this section, we describe some typical studies on polymer spinodal decomposition performed mainly to test the theoretical predictions mentioned in the preceding sections. We do not intend an extensive or complete survey of related papers. 

A.E.Nesterov, Y.S. Lipatov, Phase condition of polymer solutions and mixtures, Naukova dumka,... 

Adsorption and surface segregation from polymer solutions and mixtures... 

This Report is divided into three main sections. The first covers theoretical aspects and attempts to update existing reviews by which the topic is already well served. The second deals with methods for obtaining thermodynamic data, a topic largely neglected by review literature for polymer systems. Remarks more appropriate to particular types of polymer system are gathered in the final section. This section concludes with a source table for data on individual polymer solutions and mixtures as culled from the 1977/8 literature. While it is hoped that this tabulation is as complete as possible, omissions are inevitable and this Reporter would be pleased to receive notice of such so that they can be included in future Reports. 

By allowing the (volume) fraction of holes to be temperature and pressure dependent, lattice gas models are able to interpret thermal expansion and compression coefficients in thermodynamic functions for polymer solutions and mixtures. Onodera has developed such a model with which he examines changes of volume on mixing and pressure dependence of critical temperatures. 

Heidemann et al also presented a discontinuous method to calculate spinodal curves and critical points using two different versions of the Sanchez-Lacombe equation of state and PC-SAFT. Moreover, Krenz and Heidemann applied the modified Sanchez-Lacombe equation of state to calculate the phase behaviour of polydisperse polymer blends in hydrocarbons. In this analysis the polymer samples were represented by 100 pseudo-components. Taimoori and Panayiotou developed a lattice-fluid model incorporating the classical quasi-chemical approach and applied the model in the framework of continuous thermodynamics to polydisperse polymer solutions and mixtures. The polydispersity of the polymers was expressed by the Wesslau distribution. 

Furthermore, the phase behavior of polymer solutions and mixtures is more complex than that of small molecule mixtures. Whereas most small molecule solutions exhibit only an upper critical solution temperature phase transition, at which phase separation occurs with cooling, polymer mixtures commonly exhibit a lower critical solution temperature phase transition, at which phase separation occurs with heating. 

Several assumptions were made in using the broad MWD standard approach for calibration. With some justification a two parameter equation was used for calibration however the method did not correct or necessarily account for peak speading and viscosity effects. Also, a uniform chain structure was assumed whereas in reality the polymer may be a mixture of branched and linear chains. To accurately evaluate the MWD the polymer chain structure should be defined and hydrolysis effects must be totally eliminated. Work is currently underway in our laboratory to fractionate a low conversion polydlchlorophosphazene to obtain linear polymer standards. The standards will be used in polymer solution and structure studies and for SEC calibration. Finally, the universal calibration theory will be tested and then applied to estimate the extent of branching in other polydlchlorophosphazenes. 

One major question of interest is how much asphaltene will flocculate out under certain conditions. Since the system under study consist generally of a mixture of oil, aromatics, resins, and asphaltenes it may be possible to consider each of the constituents of this system as a continuous or discrete mixture (depending on the number of its components) interacting with each other as pseudo-pure-components. The theory of continuous mixtures (24), and the statistical mechanical theory of monomer/polymer solutions, and the theory of colloidal aggregations and solutions are utilized in our laboratories to analyze and predict the phase behavior and other properties of this system. 

Fig. 14. Comparison of the cell growth in an individual polymer solution and ATPS. The composition of ATPS was 4.5% PEG 20,000 and 2.8% crude dextran which was a mixture of 15% PEG 20,000 and 2.8% crude dextran solution in the mass ratio of 1 2.33 [83]...

Before discussing theoretical approaches let us review some experimental results on the influence of flow on the phase behavior of polymer solutions and blends. Pioneering work on shear-induced phase changes in polymer solutions was carried out by Silberberg and Kuhn [108] on a polymer mixture of polystyrene (PS) and ethyl cellulose dissolved in benzene a system which displays UCST behavior. They observed shear-dependent depressions of the critical point of as much as 13 K under steady-state shear at rates up to 270 s Similar results on shear-induced homogenization were reported on a 50/50 blend solution of PS and poly(butadiene) (PB) with dioctyl phthalate (DOP) as a solvent under steady-state Couette flow [109, 110], A semi-dilute solution of the mixture containing 3 wt% of total polymer was prepared. The quiescent... 

The applications of colloid solutions are not restricted to paints and clay. They are also to be found in inks, mineral suspensions, pulp and paper making, pharmaceuticals, cosmetic preparations, photographic films, foams, soaps, micelles, polymer solutions and in many biological systems, for example within the cell. Many food products can be considered colloidal systems. For example, milk is an interesting mixture containing over 100 proteins, mainly large casein and whey proteins [6,7]. 

As mentioned previously, Reed and Carpenter (7) suggested that a two-phase mixture of an aqueous polymer solution and a microemulsion could be used to displace residual oil while simultaneously... 

The lattice fluid equation-of-state theory for polymers, polymer solutions, and polymer mixtures is a useful tool which can provide information on equa-tion-of-state properties, and also allows prediction of surface tension of polymers, phase stability of polymer blends, etc. [17-20]. The theory uses empty lattice sites to account for free volume, and therefore one may treat volume changes upon mixing, which are not possible in the Flory-Huggins theory. As a result, lower critical solution temperature (LCST) behaviors can, in principle, be described in polymer systems which interact chiefly through dispersion forces [17]. The equation-of-state theory involves characteristic parameters, p, v, and T, which have to be determined from experimental data. The least-squares fitting of density data as a function of temperature and pressure yields a set of parameters which best represent the data over the temperature and pressure ranges considered [21]. The method,however,requires tedious experiments to deter-... 

Regular solutions are mixtures of low molar mass species with Aa = Ab= 1. Polymer solutions are mixtures of macromolecules (Aa = A 1) with the low molar mass solvent defining the lattice (Ab = 1). Polymer blends are mixtures of macromolecules of different chemical species (Aa 1 and Ab > 1). 

---