Research Point 1 Chevreul's Colour Theories

In 1824  French chemist Eugene-Michel Chevreul was employed as director of dyes for Gobelins Tapestry Manufacturers. While in this position he made intensive investigations and analysis into colour - because of complaints by customers about the dyes being used. He determined that  troublesome colour  interactions were the cause. His most influential contribution to the art world were the three colour theory laws of simultaneous and successive contrast and optical mixing.These discoveries formed part of his famous publication The Principles of Harmony and Contrast of Colours.
1.Simultaneous contrast is an optical illusion created when different tones or colours are placed alongside one another appear to lighten or darken them far more than if they were placed separately  In the case where two similar colours are juxtaposed the complementary of each will affect the other ie. red will irradiate the surrounding space with its complementary (green), but if placed next to a similar colour (orange) the red will appear more violet by a blue (complementary) cast caused by the orange. If placed next to violet, red is more orange due to the yellow (complementary) cast from the violet. Warm colours appear warmer when placed next to a cool colour and vice versa, a dark colour appears darker placed next to a light colour and vice versa. Pure colours and greys alongside one another become more intense. This effect will be immediate.
2. Successive contrast is concerned with after images and optical mixing. An after image is observed after looking at a colour for a while and upon turning away the eye sees a halo effect (or after image) which is the complementary of the colour originally observed. Optical mixing is when two different colours laid side by side produce the impression of a third colour. This is most noticeable when colours are viewed from a distance appearing to produce a combination of the first two colours ie.  primaries - red and yellow = orange, harmonious - blue and green = turquoise. This more pronounced when the colours are viewed from an angle, the further away the colours are observed the more muted the colours become.

These theories led to his development of a colour wheel divided into 72 segments, each one containing 12 main colours, divided into 6 zones around a white inner circle.

Link to experiments with grays http://www.colorisrelative.com/bwbox.html

How did particular artists use Chevreul's theories to expand the possibilities of painting?

Camille Pissaro was a great enthusiast of Chevreul's theories and through this he became a major influence in the development of Impression, a characteristic of which was to use juxtaposed dabs of complementary colour. Eugene Delacroix was another great enthusiast of Chevreul's and he also had a significant effect on Impressionism, experimenting with broken tones in his quest for vibrant and luminous colours. The impressionists followed his methods on optical mixing using broken colour to give an impression of light. Pissaro in turn also influenced  Neo or  Postimpressionist painters to further advance the technique by using a multitude of dots to apply pure pigment.What had been the quite spontaneous methods of the Impressionists became more exacting and scientific in the hands of the Postimpressionist such as Signac, Seurat, Cross and others who also made direct reference to Chevreul's theories. Pissaro adopted this style  in 1886 for a time.  As did Edouard Vuillard - see http://www.wikipaintings.org/en/edouard-vuillard/studio-interior-model-for-the-scenery-of-la-lepreuse#supersized-artistPaintings-241631 
By using Chevreul's teachings on colour theory and simultaneous contrasts Robert Delauney  created a new technique  producing sensations of pure colours in depth and movement. starting with recognizable objects and gradually becoming increasingly abstract. It became known as Orphism.
Other artists later exploited the effects of optical mixing, including Sigmar Polke 'Girlfriends' and Roy Lichtenstein 'Masterpiece 1962'.