so the materials that do have a lot of technological importance are liquid crystalline materials and as I mentioned they have long range orientational order but not the positional order and just to tell you a little bit about the history again how these materials were discovered so it actually happened relatively early on in 19th century what was discovered is that if you take a particular type of a material called cholesteryl ester and if you measure a heat flow as a function of temperature using a method called DSC are you familiar with this technique you have used it in 301 for what is the Essene differential scanning calorimetry that's right so what you're measuring is you are basically measuring what is the heat flow that is required to keep the material at a certain temperature right so if you if you start from a relatively low temperature this material will be solid and at a certain temperature again for this particular material what happens it happens to be at one hundred one hundred and forty-five degrees the material goes through a phase change and you can see this from this peak in the DSC scan and it turns out that this material becomes haze and it flows and if you continue you would have yet another peak and the material will become transparent and liquid so this was just a standard type of a material or let's say crystalline material it would have only one particular peak because it would transition from solid to liquid but certain types of materials can exist in the liquid crystalline phase what this tells you is that the material itself can have a solid crystalline form it will transition to a new state of matter called liquid crystalline State and then you increase the temperature it will become completely liquid right so these are just three different forms of the same type of material that can exist at different temperature ranges okay so what is the difference or what is what is really happening is that in the solid phase again these molecules will be will have the same orientation and it will be precisely position in space so this would be the crystalline form when you increase the temperature this positional order would be destroyed but the molecules because they're highly anisotropic will still have this orientational order and when you increase the temperature and you come to this temperature range which again for this particular material happens around 170 degrees you will eventually have the material that is completely liquid like right so even this orientational order is lost okay so liquid crystalline materials as I already mentioned have highly anisotropic shapes of the molecules that constitute them so these are either very long molecules they can have discs like shapes or some of them they're so-called banana liquid crystalline materials but what they all have in common is the fact that they highly anisotropic what that means is that one dimension is significantly larger than other dimensions of that particular molecule so in the case when you have a material or the molecule that where the length of the molecule is significantly larger than the the diameter this is a cold rod bike or climatic so when you hear a bird Kalama take liquid crystalline material it simply means that the molecules that constitute that material are rod-like so the then if they have this claw ship so what that means is that the diameter is significantly larger than the height of the molecule so this is this like so these will be called discotheque again our dimension there are other types of but these are the most common so the kilometer and discotheque liquid crystalline materials are the most common ones okay so the summer is about what we learned about general order in crystalline liquid crystal and etc materials what we know is that for solid crystalline materials we have both positional and orientational order for plastic crystals we do have the positional but we lack the orientational order for the liquid crystals it's the opposite case so the orientational order is preserved and for is a tropic liquids we don't have either right but again the message is that a given material or a given molecule can form one of these forms so again the plastic crystals as I mentioned are typically spherical but if you have anisotropic it can as a tropic molecule it can form either a liquid liquid crystalline and stop it and one not before also we move ahead is just to say that in the liquid crystalline materials this orientational order is usually averaged over time so if you take a snapshot of a liquid crystalline material in time you will rarely see really perfectly aligned molecules but on average over time you will see a certain orientation okay so this is just one thing to remember as you come forward so general terms in terms of for the calamity or rod-like type of a crystalline materials that you'll have a general form and this is typically a set of aromatic rings that are connected with these different types of connecting units and they can be functionalized their ends using different types of terminal functional groups and again they can be decorated on sides with different types of side groups and and etc in general terms they are this these types of automatic types of structures and you can arrange them in different ways and then the side groups themselves will tell you how likely this material will be to exist in the liquid crystalline form how likely to perform this orientational order etc again the reactivity of the end groups will tell you also how likely is that this material will eventually form a crystal and material how it will react with surfaces interfaces other materials etc so you can actually play with these materials and engineer the liquid crystalline materials with different properties okay so because they have this relatively unique properties the question is how do we describe their structure right so I mentioned the fact that the power distribution function in principle can be used for these materials but it's not necessarily the best way to describe them so in the field of liquid crystalline materials there is one particular descriptor that is very often used and it's called the director so the director will be an average orientation of the molecules in the liquid crystalline phase so if you look look at this liquid crystalline material you will see that again on average the orientation of the molecule is roughly in the same direction but very small variation right so each molecule has its own direction which we'll call P I and this is a non-polar vector so it simply tells you the orientation but not a direction so it simply tells you well this particular molecule it has certain orientation but we don't necessarily know anything about the direction right so we don't actually care about this so the director itself will be defined as a non polar vector that describes the average of the orientations and it will be indicated with this + symbol and what the simple symbol simply means is that this is an average of P ice over volume so if I for example have a certain non polar vector P I and if this is my director and this P I will be defined by an angle theta I so again the average theta for this particular crystal will be zero because on average the orientation of the molecules is along the director line but each molecule will have a small deviation from that angle so I can also ask you a question why did I write why did I write this as n as a function of R so why is this director a function of the position right R is the position within the material what does it mean one thing that can help you is try to look at this optical image of a liquid crystalline material so this would be an optical image of a liquid crystalline material and it has different colors in different areas so why did I write the director is a function of the position the director itself is locally defined what that means is that if you have a material liquid crystalline material the orientation locally so this was my liquid crystalline material then I can have different domains that are not necessarily strictly separated they can be continuous but the orientation of the molecules is locally defined what that means is that in this area the molecules will have for example horizontal orientation and therefore the director will be in the horizontal direction here there may be slightly different there will be completely different etc and the colors in this image actually represent the change of the director so when you look at the liquid crystalline material through either polarized light or using optical microscopy the optical signal will depend on the orientation of the director again what that means is that locally in this particular area here in blue region I know that all of the molecules and there are many of them here right they have the same orientation but when I move here this orientation slightly different and if you made this liquid crystalline material very small this is for example what is used in liquid crystal in the space you're trying to make one individual domain right so you're trying to make this domain such small that the director is unique to the entire region of the crystal okay do you have a question in principle yes so you're in the magnetic domains you're also talking about the orientations of the spins and this can be rotated or in an you know it can be arranged in different ways but in a local area there are all arranged in parallel and it's a good analogy right the physics is completely different though but the analogy stands there okay so again the take-home message is the director is the way to describe like with crystalline materials and when you look at them in so-called pneumatic liquid crystalline materials which are that the liquid crystalline materials that we defined so far but there is no positional order but there is long-range order when you actually look at the director so the director would be in this direction and what that simply means is that when you look at the frequency or the number of the molecules that have a certain orientation and if this was the the angle of the director so what that means is that if this is my zero orientation and I know that the director is here I'm sorry this would be yes the director is in this direction this would be the angle of the director what that means is that most of the molecules if I plot their orientation which is the angle between each molecule and the director they would be all very closely focused around this particular angle right so there would be a distribution that is relatively narrow meaning that most of the molecules have exactly the same orientation as the director and average there is small distribution but it's relatively narrow okay so how would this graph look like if I heat this material so if I increase the temperature so they so this is the the pneumatic liquid crystal it has this particular distribution and if you increase the temperature how would this graph change because it would be wider until you have just flatline right if this was a liquid you would simply have a line what that means is that there is no preferential orientation of the molecules okay so again this already tells you that the descriptor itself is very useful descriptor for the case of the liquid crystalline materials but in for the liquids themselves the director doesn't have any meaning right so again this really emphasizes the fact that for particular types of materials you have to think about the best and the most appropriate way to describe them so