For each mixture the phase transition has to be recorded as function of temperature in order to determine the transition temperature. Similar questions arise for other multiphase materials such as crystalline systems. In many cases, in addition to the transition temperature, the time development of the phase formation (e.g. in isothermal experiments) is also of interest.
Small angle light scattering as a method to detect phase transitions
During a phase transition (e.g. in polymer mixtures) domains of a second phase are formed in a formerly homogeneous sample. Vice versa, phase domains dissolve and the sample becomes homogeneous. It is well established, that such changes can be detected by light scattering with high significance. Light scattering delivers not only information about the appearance or disappearance of phases, in addition information about size and shape of the phase domains can be obtained, which are of importance for many of the material properties.
Light scattering is originated by samples with inhomogeneities in composition or density with size in the range of wave length of light. Such inhomogeneitis may be particles or phase domains. Both are referred in the following simplified as “particles”. The incident light is scattered in all directions. Depending on size and shape of the particles and polarization of the incident light the scattering intensity is a function of the angle θ between the incident and the scattered beam. The scattering pattern of homogeneous spherical particles or statistically oriented particles of arbitrary shape are radial symmetrical and the scattering intensity depends in this case only on the angle Θ. The scattered intensity is typically expressed as a function of the scattering vector q, which is a function of θ:
where n is the refractive index of the matrix phase, and λ is the vacuum wave length of the laser. Theoretically obtained intensity vs q curves (Mie-theory  or Rayleigh-Debye-theory [2, 3]) are shown for spherical particles of different radius R in Fig. 1.
It can be seen, that the average scattering intensity at small values of q (i.e., small angles θ) increases tremendously with increasing particle size. The positions of the intensity maxima and minima shift simultaneously with increasing R to smaller q-values, whereas the shape of the intensity vs. q curves remain self-similar and scales with R. In the case of size distribution of the particles or multiple scattering, the curves in Fig. 1 are smoothed, since the minima and maxima are smeared out. For statistically oriented non-spherical particles the intensity vs q curves (scattering function) represent “shape-averaged” values. For this case the scattering function of spherical particles are assumed as approximation to obtain size information from the scattering data.
High-Throughput Determination of Phase Diagrams
To speed up the establishment of phase diagrams, a temperature scan is applied to a large number of mixtures simultaneously. The individual mixtures are contained in the wells of a micro well-plate with up-to 96 wells, or are applied separated from each otheron a flat glass substrate. The samples are positioned in a temperature controlled oven, which is programmable to realize increasing or decreasing temperature ramps. An inert atmosphere to protect the samples against oxidation is provided by a continuous flow of argon or nitrogen through the oven. Quartz glass windows are embedded in the oven walls opposite to the top and bottom face of the well plate to allow the illumination of the samples by a laser beam (wavelength: 488 nm) and the detection of the scattered light cone. The optical system is consisting of the laser and the detection unit (lens system plus CCD-camera). It is designed as a movable assembly outside the oven and can be positioned by motorized x-y micrometer stage. To prevent for pronounced heat loss the oven windows are shielded by heating plates moving together with the optical system. Apertures in the heating plates allow the incident laser beam and the scattering cone to pass through. The apparatus is sketched in Fig. 2 and a photo is shown in Fig. 3.
During the temperature ramp the scattered light of each sample of the well-plate (or of the separated samples) is detected by positioning the optical system accordingly.
As an example for high-throughput determination of phase behavior, different styrene-butadiene rubbers (SBR) mixed with a terpene phenolic resin (SYLVARES TP2040, Arizona Chemical), are studied. By varying in the amount of styrene within the SBR, a so-called compatibility map was established. In this case, the map shows the phase transition temperature as function of styrene content of the SBR and the mixing ratio of the SBR with the resin. The samples were provided by Michelin. For high-throughput sample preparation, a robot system developed at the University of Jena (Germany) was used.
Thirteen SBR samples with different amount of styrene were studied. For each SBR type, seven resin mixtures with SBR amounts of 10, 20, 30, 50, 70, 80, and 90 % were prepared. The resulting 91 mixtures were dispensed in a micro well-plate and the phase behavior was studied in a temperature range of 25 to 140 °C. The well-plate was therefore heated up to 140 °C with a ramp of 2 K/min, followed by a cooling ramp of -2 K/min. The phase transition temperatures were determined during cooling.
Fig. 4 shows exemplary the scattering patterns for all resin mixtures with SBR1 (containing 4 % of styrene) at the beginning (140 °C), two intermediate temperatures (85 and 52 °C), and the end of the cooling ramp (25 °C). Comparing the scattering patterns at 140 °C with those at the lower temperatures, it can be seen that the patterns of the mixtures with 10, 20, 70, 80, and 90 % SBR1 exhibit the lowest intensity at 140 °C. It is therefore assumed that these mixtures are in the homogeneous state at that temperature. The pattern of the 50 % mixture does hardly vary with temperature. This means, the 50 % mixture remains phase separated in the studied temperature range. For the mixture with 90 % SBR1 the intensity has slightly increased at 52 °C, which is indicating the onset of phase separation.
Fig 5 shows the circularly averaged intensity as function of the scattering vector q for the mixture of 90 % SBR1 at 140, 52, and 25 °C. According to the 2D pattern in Fig. 4 the intensity at 140 °C is low and originates from parasitic background scattering. The slight increase in intensity for q-values in the range of 1 to 2.5 µm-1 at 52 °C is caused by scattering on the domains of the emerging second phase. At room temperature the mixture is expected to be more apart from the phase transition temperature (i.e., “deeper” in the two-phase region). Correspondingly the larger domains result in a higher scattering intensity.
As a visual tool to identify the phase separation temperature for each mixture, the circularly averaged intensities are color-coded and plotted in a q versus temperature (x-coordinate) diagram. The resulting colored intensities are shown in Fig. 6 as a function of temperature during heating up to 140 °C and a subsequent cooling ramp exemplary for the mixtures with 20 and 90 % SBR1 with 4 % styrene. The onset of phase separation is indicated by an orange arrow.
The phase diagram of the SBR1/resin mixture is shown in Fig. 7. It resembles the typical shape of a binary mixture with miscibility gap featuring an upper critical temperature. This upper demixing temperature for the SBR1/resin corresponds to a 50/50 mixture and a temperature of 140 °C.
Arranging the phase diagrams obtained for each of the SBR types containing different amounts of styrene together, a compatibility map is obtained. It is shown in Fig. 8. For mixtures with compositions in the white areas the phase state could not be determined clearly. Reasons might be failures during preparation such as contamination by dust or droplets that had not been dispensed properly while filling the well-plate.
The compatibility map shows that the miscibility of SBR and resin increases with increasing styrene content of SBR. For example, the upper demixing temperatures of resin mixtures with SBR-types containing more than 25 % styrene are less than about 125 °C and it will be even lower, in the range of only 100 °C for mixtures with SBRs containing about 33 % styrene.
A high-throughput small-angle light scattering (HT-SALS) method to speed-up exploring phase behavior of complex mixtures has been developed at plastics division of Fraunhofer LBF. Phase diagrams and compatibility maps for styrene-butadiene rubber (SBR)/resin mixtures are established. Temperature and composition dependent mixing behavior is exhibited by many types of materials or formulations. This includes adhesives or formulations for paints or coatings. The developed method cannot only be applied to polymeric systems but it can also be used to determine phase behavior of pharmaceutical recipes or formulations belonging to cosmetics or food. It is furthermore possible to monitor the formation of solid phases in systems being completely liquid at the beginning (e.g. in isothermal or pseudo-isothermal experiments). Such experiments are relevant for drying of coatings or crystallization from liquid phase or melt.
The project – initiated by Michelin to characterize rubber mixtures – was supported by the Dutch Polymer Institute (DPI) by the grand No. 729. We would like to thank Jürgen Vitz and Ulrich Schubert from Laboratory of Organic and Macromolecular Chemistry (IOMC), Friedrich Schiller University Jena (Germany), for the sample preparation and the successful collaboration.
 Mie, G.: Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen. Ann. Physik 25, 377 (1908).
 Kerker M.: The Scattering of Light and other Electromagnetic Radiation. London: Academic Press, Inc., 1969.
 Van de Hulst. H.C.:Light Scattering by small Particles, New York: Dover Publ., 1981.
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