Can I make my own graphene at home in my kitchen?
I Googled the phrase "How to make graphene" and got this result, which contains a section on how to make it at home.

The answer is, unequivocally, yes you can. Below are excerpts from the linked page.


  (1) The first DIY method is to use a lead pencil to deposit a thick layer of graphite onto a paper. Then use ordinary sticky tape to peel off a layer of graphite from the paper. Use another piece of sticky tape to remove a layer of graphite from the first sticky tape. Then, use a third piece of unused sticky tape to remove a layer from the second piece of sticky tape, an so on. Eventually, the graphite layers will get thinner and thinner, and you will end up with graphene, which is single-layer graphite in the strict sense, or bi-layer or few-layer graphite (which acts almost like graphene in certain uses). Even though this way of making graphene is only a proof-of-concept, the sticky tape method works. It takes patience and time, but it's the DIY method which the Manchester group used in 2004. And remember, they actually won a Nobel prize for their work, so there's no messing with sticky tape!
  
  (2) Shear exfoliation in liquids starts by pouring powdered crystal in a liquid, and then using a shear mixer to separate (exfoliate) layers of material from the crystal. The liquid that is used in such processes is chosen so that the small graphene particles don't clump back together, and the result is a liquid suspension of graphene. The suspension can then be dried to obtain graphene nanoflakes, or it could be directly used in later technological processes, such as making of graphene coatings and others.
  So, how do you make graphene at home using this method? Well, you can replace the shear mixer with a kitchen blender (since shear mixing is a fancy word for high-tech blending), and instead of special liquids you can use water and dish detergent. The detergent is added so that the particles don't clump, and acts as a surfactant. A great source of graphite powder are graphite pencils. Simply powder a few pencil leads and add the powder to the detergent solution, then blend for a while. Unless you have access to special microscopes and other equipment, you will probably be unable to confirm the existence of graphene in your detergent solution, but there's a quick rule of thumb which you can use to estimate the particle size. Generally speaking, if the graphene particles are too big, they will sink to the bottom of the vessel, while if they are smaller, they will float to the top. Nanoparticles are so small that they will be suspended in mid-water, and this is what you're aiming for if you want to make graphene. After you make enough graphene particles, you might want to filter the suspension and leave it to dry.
  
  (3) If you pour a non-water-soluble liquid into water it will either float on top of the water, or the water will float on top of it, depending on whether the added liquid is heavier (more dense) or lighter (less dense) than water. A common example is oil floating on top of water. One group of scientists discovered that you can make graphene by pouring two solvents which do not mix together, such as heptane and water, into a glass and adding finely ground graphite powder and putting it in a sonication bath. You can buy heptane in most chemical supply stores, water is readily available (it's a good idea to use distilled water), and you can easily obtain graphite sticks in art shops. An ultrasound bath is needed, but these are not uncommon on ebay and the like. The resulting graphene is one to four layers thick, and is chemically stable. It can be extracted and deposited on a clean glass plate, or any other substrate. The idea is to mix the finely ground graphite with water and heptane (1:1 ratio of water and heptane) and sonicate it for a while. What happens next is that graphite flakes exfoliate at the interface between water and heptane and graphene actually starts "climbing" up the glass walls of the vial. If a hydrophilic substrate, such as a glass slide, is introduced through the interface, a thin film of graphene will climb the walls of the slide as well. The glass slide can then be extracted and after drying, you'll be left with graphene-coated glass. If you use a polyethylene vial, the resulting graphene will not climb the walls of the vial, but you can still extract it with a slide made of glass or other hydrophilic material. Graphene is deposited as a thin film on both sides of the glass plate, and its slight light-absorbing properties can be seen by looking through it (Graphene absorbs about 2.3% of visible light). The explanation of the process is that graphene self-reassembles from the small exfoliated flakes on the interface between water and heptane because the surface tension of graphene (54.8 mN/m) is nearly right between the surface tension of water (72.9 mN/m) and heptane (20.1mN/m). The thickness of the graphene film is limited by capillary forces on the interface and the excess graphene will simply fall to the bottom of the vial. The formation of thick aggregates is suppressed by the diffusion and the energy requirement needed to form a new layer. This is possibly the easiest way to make DIY graphene at home as an arbitrarily large sheet. Other methods only create graphene flakes, but these flakes could possibly be used instead of graphite flakes in this method as a refinement stage.