I extracted organic matter using H2O2, then ultrasonic bath, sieve 0,053mm, after centrifuge 10.000 rpm 4 minutes, If you do not need all clay, You take how much supernant you need, do this step as many time you want, then dry, and You have clay without chemicals.
in some cases (agricultural soils mainly) I managed to collect enough material for XRD just by keeping soils in distilled H2O for several hours than shaking the suspension for several minutes (in a closed vessel, of course, e.g. centrifuge cuvette) than separated the clay by sedimentation. After most of the clay was collected by repeating previous method, I used ultrasonic shaking for 1 min of the collected suspension than repeated the sedimentation. The final clay suspension I extracted by centrifuging, there you may also opt for grain size separation below 2 micrometers. But if you find a "standard and approved " method, please let me know :)
There is a method be used without adding or using any chemical to ur clay. About 250 grams of clay were poured into plastic containers with adding de-ionised water (distilled water). Left for one hour, the large particles setteled out, and the resulting suspension decanted into clean tubes to a height of 30 cm. the tubes were supported in a water bath and all tubes for different clay types must be labelled. left for another hour cover the tube by cling-film to avoid any contamination. Stoke's Law be applied for clay size separation. When size fractions have been separated, the sample transferred to into appropriate clean centrifuge vessels (above 3000 rpm) for 10 to 15 minutes. Remove the residue solid in the bottom of the vessel by using a rotamixer with adding small amount if deionised water. Drying of the samples using the freezer dryer technique, after that the clay samples become ready for mounting for any kind of test e.g XRD analysis to identify the clay minerals and non-clay minerals available in your samples.