I have found some text dealing with different types and examples of transitions in DSC maybe it can help you.

http://www.masontechnology.ie/x/Usercom_11.pdf

Dear Sanjoy Paul,

LCPs are characterized by their instantaneous LC-transformations during heating or cooling. So, calibrations are essential. See e.g. attached link, which is hopefully relevant.

Article Transformational kinetics in liquid crystal polymers and dif...

Dear Paul

The event is also time dependent. However, if the samples have a good quality (no dusty, etc) the Tonset is nearly the same of Onset of crystallization. To describe this is necessary to consider the intermolecular attractions, nature of molécules - organic polar, apolar, perfluor and so on, Upon cooling we have to allow of all atoms in the molecule search for the best position in the crystal lattice. So, think what happen if the molecules have a long alkyl chain, as in the LC system. How is the probability of all the atoms in the chain attract mutually in the such way that the final arrangement is the best? It is impossible due to the apolar nature of the chemical bonds. This is a preliminar ideias.

Please see the article attached

Aloir

The signalled behaviour can be generally expected when the studied phase transition does not occur at a well-defined equilibrium temperature, but rather during a temperature range, while the substance is being cooled or heated. Such a transition typically shows a noticeable kinetic dependency and a non-equilibrium character that associates with non-linear features of the transition. Such features are typically signalled by a noticeable heating (or cooling) rate dependency and by hysteresis on a heating-cooling cycle (or vice-versa). These are well-known features of the glass transition, as shown at the heat capacity vs. temperature plot depicted as Fig. 1 from the following paper:

Article Aspects of the non-crystalline state

Very nice paper Dr Queiroz

Dear Sanjoy Paul,

I make two preliminary remarks and ask three questions.

1. Your graph shows for cooling/heating two peaks that can be linked to LC transformations.

2. The other peaks seem to be slow as compared to the set cooling/heating rate.

3. What is the cooling/heating rate applied?

4. What is the LCP you are studying?

5. Are you planning to study these transformations as a function of the  cooling/heating rate?

Looking at your scans , I suggest adding isothermal step (at both ends) before changing heating to cooling , to allow for temperature lag compensation, can improve your results. Secondly running both experiment with different scan rate will also help to understand system. 

All of these tips are technical advice. The origin of phenomena is molecular.

The difference in the transition temperatures obtained from the two curves results from overheating, undercooling phase transition and the temperature hysteresis in the DSC test.

You have to explain the origem of hysteresis. It is time-dependente, it is rate heating dependente; it-  is 

This is due to super-cooling. If you go to smaller and smaller heating and cooling rates, the difference should vanish. Super-cooling is a kinetic effect in the thermodynamics of phase transitions.

can we determine VPTT of microgels by DSC? please suggest me some papers

Usually,

During endothermic process material consuming (enery absorbtion) little more energy than exothermic (energy release )process

Supercooling and Superheating for crystallization. LC-LC transition shows a smaller supercooling and superheating. Transition temperature should be evaluated by onset temperature rather than peak.

From your case, it could be from the different crystal phases about liquid crystal materials at low temperatures because it should be taken into both factors of kinetic or thermodynamic control from the heating or cooling cycle.

This is due to the enantiotropic and monotropic nature of the liquid crystalline materials. This causes the smaller values of phase transitional point in cooling when compared to heating.