The crystallinity of polymers, in general, related to aging process due to recycling process of different temperatures. 

By fast cooling  from melting state the semi crystalline polymers have  a completely amorphous structure.  By reheating begin the crystalline to form again in this state called recrystallizing. As the temperature is reduced below the glass transition temperature, the crystallization  rate decreases rapidly because the molecules have lower movement to reach the relaxation state. In this case you can show the glass transition temperature and cold crystallization.  The density  of polymer is increased as the crystal structure of polymer  forms from amorphous  to  crystalline.  Control of the crystallization process depends on control of the cooling rate , i.e. optimize the cooling rate help the crystallization from melt and the size of spherulite is reduced than very lower  cooling. This is required in industry by manufacture sheet film. When semi crystalline polymer is annealed , the crystalline part and its density  is increased, because the  lamellar thickness increased by longer annealed time near melting point.

Thanks for comments Ahmed Mohamed El-Hadi ......How you see the following plot as apparently it contradicts what you described in your comment. In the plot PM-5 is solution cast film, while PL-5 and PLLL-5 represents 5min and 15min anealing followed by chilled water quenching. There is a cold crystallization peak (1st peak) which defintly need to subtract when calculating %crystallinity but still crystallinity for solvent cast film is lower than anealed sample folled by quenching.

In DSC measurement in the first run(first heating) the crystallization ratio is smaller than in second run (second heating) . This depend on the preparation of the sample from solution (history of sample).  By second run the sample was placed in Aluminum pen and then heated and then crystallization. The crystallization condition is different. You make annealing  at any degree.??????, but there are no change in the degree of crystallization in sample PL-5 and sample PLLL5. You must write the history for each sample , where the first run , cooling run and second run, because  the crystallization percentage is calculated from second run. I think,  you have 3 runs in figure.

Dear Imran Khan,

I think that for a proper discussion it would be worthwile to reformulate your question as clear as possible and preferently as close as possible linked to your experimental data, full information of the polymer (nano)composites included.

dear P. Van Mourik....I think i make the question prety straight forward. Anyways,The nanocomposites composition is Poly lactic acid with carbon nanotubes. I am asking is it possible in a solution cast film, when further processed to control crystallinity , through anealling and quenching technique increase crystallinity. As annealing should decrease crystallinity evidenced from litrature.

Dear Imran Khan,

Being retired I cannot pretend to be an expert on PLAs. Nevetheless I make the following remarks.

1. All the DSC runs shown were taken at heating (rate?).

2. For the group of PLAs it holds that the crystaillinity is mainly determined by the ratio of l/d enantiomers.However, PLA of your study is nearly pure l-type, given the melting point indicated by your DSC runs.

3. I assume that the PM-5 run was taken just after condensation and before adding the carbon nanotubes.

4. Furhter I assume that annealing of the specimens for the PL-5 and PLLL5 DSC runs took place at temperatures just below the range of the melting temperatures and that the volumefraction of the carbon nanotubes for these specimens was equal.

5. Then based on the data of your DSC runs the following preliminary conclusions arise:

5.1 Apparently cooling after condensation can effectively suppress crystallization (your DSC run for PM-5 does not show any sign of a crystallization effect; clearly the melting peak in this DSC curve fully represents the amorphous phase of PLA.

5.2 Increasing the annealing time from 5 to 15 min yields an increase of the content of the crystallization peak as occurring in your DSC curves.

5.3 However, the phenomenon mentioned in point 5.2 seems a minor effect: there is no significant difference in the magnitude of the heat content of the melting peak for the PL-5 and PLLL5 in the respective DSC curves, albeit larger than for PM-5. Further it should be remarked that the maximal value of crystallinity seems mainly be determined by the geometry of the enantiomers concerned and perhaps by the form of the carbon nanotubes. The models for crystallinity in semicrystalline thermoplastics (fringed-micelle or spherulite) may be helpful for further understanding and study.

6.  Apparently, your initial question: Does annealing followed by quenching (chilled water) always result in a decrease of crystallinity in polymer nanocomposites ? has for the time being  a negative answer. I note that questions with the word 'always' need only one case to negate the content of such questions.

7. Good luck with the continuation of your research and studies!

 Dear P. Van Mourik , bundle of thanks for valueable comments . Hope it can help to direct my way towards right approach.