According to my understanding, smaller size of particles will reduce the electrical conductivity. As the size goes to nanoscaled, there might be some kind of quantum confinement effect, which would significantly affect the electrical transport. You can find a lot of papers about this. Just my guess.

I am also not sure what particle size and what polymer you mean:

- if conductive polymers, the primary particle size which has a big influence on conductivity is given by the polymerisation and roughly 10 nm; the better the particles are dispersed, the higher the conductivity

- if you mean conductive fillers, then again, the conductivity is better the better the dispersion.

You can find many publications in my RG page, maybe one step into this field could be this publication:

https://www.researchgate.net/publication/49593603_New_Insight_into_Organic_Metal_Polyaniline_Morphology_and_Structure?ev=prf_pub

and / or:

https://www.researchgate.net/publication/237099364_Dispersion_as_the_link_between_basic_research_and_commercial_application_of_conductive_polymers_(polyaniline)?ev=prf_pub

and / or:

https://www.researchgate.net/publication/229816762_Electrical_conductivity_in_heterogeneous_polymer_systems._V_(1)_Further_experimental_evidence_for_a_phase_transition_at_the_critical_volume_concentration?ev=prf_pub

(but there is much more, please look yourself what could help you)

For a given conductor, like a metal, as Kun Zhang already mentioned, the conductivity decreases when the particle size gets below 1 µm. Please look for literature with the main author Gunther Nimtz (Univ of Cologne). I have worked with him as well after I had found his publications (he had shown this phenomenon for metallic particles), and we investigated conductive polymers together and found that they behave the same, here just one of several publications we have made together:

https://www.researchgate.net/publication/41707771_Mesoscale_charge_transport_in_polyaniline?ev=prf_pub

Article New Insight into Organic Metal Polyaniline Morphology and Structure

Article Dispersion as the Link between Basic Research and Commercial...

Article Electrical conductivity in heterogeneous polymer systems. V ...

Article Mesoscale charge transport in polyaniline

Bernhard Wessling; I agree with you , if particle size of the nano material is low , higher the conductivity .. what happens to the width of the Raman peak when the particle size decreases.... weather peak increases or decreases with the decrease in the size of naparticle size?

Kun Zhang ; I agree with your comment ,smaller size of particles will reduce the electrical conductivity but how does this effect on width of Raman peak.. ? width of peak the peak goes on increasing or decreasing with decrease in the size of the nanoparticle (filler) ?

May I first ask again, what type of conductive materials are you talking about or are you dealing with, and what conductivity of what kind of polymer are you talking about in your starting question?

semiconductor nanoparticles like SiO2 and TiO2 and the polymer like PVA

Bernhard Wessling: semiconductor nanoparticles like SiO2 and TiO2 and the polymer like PVA

pure SiO2 is a perfect insulator, I am not familiar with whether and how and to what degree one can successfully dope it to become reasonably conductive, TiO2 is a semiconductor. I would assume that - whatever would be the purpose to put them in PVA - my previous statement are also valied for them:

- the smaller the particles, the better you can get at least some conductivity into the composite

- however, the smaller the particles, the harder to disperse, but that's what you need to overcome this;

- I am not familiar with how the conductivity of semiconductor nanoparticles varies with nanoparticle size, I would not bet at all that they behave the same as metals, in contrast (because the conductivity mechanism is totally different)

For the topic of dispersion, I recommend you read this:

https://www.researchgate.net/publication/202290104_Critical_Shear_Rate_-_the_Instability_Reason_for_the_Creation_of_Dissipative_Structures_in_Polymers?ev=srch_pub

which is part 2 of the dispersion theory, and part 1:

https://www.researchgate.net/publication/202290104_Critical_Shear_Rate_-_the_Instability_Reason_for_the_Creation_of_Dissipative_Structures_in_Polymers?ev=srch_pub

Article Critical Shear Rate - the Instability Reason for the Creatio...

Tariq Bashir : when TiO2 of decreasing particle size is doped with PVA , what happens to the peak at 143.5 cm-1 in Raman study weather the peak broadens or gets sharp ?

sorry, Sunil, I don't understand this question. How can you "dope" TiO2 with PVA? do you mean you want to incorporate TiO2 into PVA?

Bernhard Wessling : yes , its treated as a filler

if I now understand correctly, you want to incorporate TiO2 (nanoparticles? how small?) into PVA. Hence you do not "dope" the TiO2 with PVA, you want to use TiO2 as a filler in PVA. What is the purpose (if I may ask, if secret, just tell me "it's secret", no problem).

The issue starts with how you want to disperse, this is the most important key step, this is why I mentioned several publications which can introduce you into this topic, please look above the various links I mentioned in my above comments.

In one of the publications ("further experimental evidence ...") you will find that after dispersion (if you do it properly) there will be an adsorbed layer of PVA (probably monolayer) on each dispersed particle.

By the way, the smallest effective particle size which you can achieve in a polymer matrix system is very much dependant upon the molecular weight of the PVA you are using - the smaller the MW, the smaller particle size you can achieve.

Let me give you an example: if you start with nano-TiO2 (primary particle size 20nm? I don't know), you will never be able to disperse them completely, you always get secondary particles in a size of around 100 nm or bigger.

If you start with 1 - 2 µm TiO2 (or 5 µm), you can achieve these particles to be totally separated and well dispersed.

Anyway, after dispersion, some PVA will strongly adsorb on the particle surface, as a monolayer (read "further evidence"!). I assume, that this will have an effect on the Raman spectrum, as these parts of the PVA molecule will not be as mobile any more as they were before, that should cause some change in the Raman spectrum, but I don't know which frequency and to what direction.

By the way, as I assume you may not have proper dispersion tools for using a PVA melt, I suggest you prepare a dilute PVA solution in an appropriate solvent, then use a ball mill or another high speed high shear mixer (e.g. Ultraturrax), then evaporate the solvent (which takes a long time at the end! may take several days under elevated temperature in vacuum to completely remove it!)

Let us know what you found out.