The fine particles have much larger surface to volume ratio (for spherical geometry A/V= 3/R  compared to large particles.  THat means surface free energy versus bulk free energy is much higher. One can easily formulate the global Helmholtz free energy optimization, which includes not only the bulk but also the surface free energy.  That produces the critical size of the particle below which agglomeration should take place if there is a mechanical contact  occurs or they are embedded into a medium which allows matter transfer between particles by surface drift-diffusion. Actually this phenomena is closely related to the capillary forces, which involves the gradient of  (Kappa x Surface Helmholtz free energy density), where  Kappa is the local curvature. One can also formulate the general problem, which involves applied stress on the ensemble of particles using global Gibbs free energy. 

Because of  the closed contact forces which are  closely correlated with the surface area versus volume ratio, which may be given by the following metric: ' '

Nanoparticles have very high surface area to volume ratio. So if you think about the surface of any material, the cohesive forces between molecules in the bulk are shared with all neighboring atoms. However, on the surface of the material there are a lot of unsatisfied atoms that do not have neighboring atoms above them. So surface atoms exhibit stronger attractive forces between their nearest neighbors on the surface. i.e surface tension. This is primarily what causes the agglomeration of NP’s as  they strive to reduce their higher surface energies by clumping together.

Thanks a lot for your helpful answers. Although your responses looks reasonable, there are some ambiguous parts on that for me .

Surface tension is a factor which is dominant in liquid state processes. Can we use this explanation for a solid state process?

I'm still confused that fine particles have more unsatisfied atom so their tendency to agglomeration is more than larger particles, while larger particles have more attractive adhesion force according to van der walls equation.  How it can be explained?

I apologize, I probably should not confuse surface tension with surface energy. Surface energy for solids is defined as the excess energy at the surface of a material compared to the bulk because of the unsatisfied atoms. Everything in nature wants to be in the lowest energy state so there is a tendency for nanoparticles to agglomerate to minimize their excess surface energy. The fact that they have very large surface area to volume ratios enhances this phenomenon. As they agglomerate they become the large particles that you mention. On the other hand, attractive adhesion forces are a completely different mechanism since these attractive forces occur between two substances by sticking together mechanically or by opposing charges. Van der waals is an intermolecular force that exists between molecules of the same substance. This type of cohesive interaction unites molecules causing them to form clusters due to their dislike for their surroundings. Van der Waals is a very weak interaction so it has a greater influence for smaller molecules at shorter length scales (consider the fact that molecules and atoms are an order of magnitude smaller than the smallest nanoparticles which might be 3-5nm). So while Van der Waals forces likely exist between nanoparticles of the same type, the mechanism that causes them to agglomerate will be dominated by stronger polar, electrostatic and covalent interactions or surface energy interactions described above.

Search for "particle coarsening" in google.. 

FROM WİKİPEDİA  What is agregate? a mass of fragments or particles loosely compacted together. OR The Latin 'agglomerare' meaning 'to form into a ball'

''The terms “agglomerate” and “aggregate” are widely used by powder technologists to describe assemblages of particles that are found in dry powders and powders in liquid suspensions. Each term has a specific meaning but, unfortunately, they are frequently interchanged at will and this has resulted in universal confusion. This confusion is perpetuated by conflicting definitions in national and international standards and this presents problems when describing powder properties or communicating results in reports and research papers. This paper reviews the current status of the definitions, with particular emphasis on their use in the pharmaceutical industry. It is proposed that just one term, agglomerate, should be used to describe an assemblage of particles in a powder and that the term aggregate should be confined to pre-nucleation structures'' 

My understanding was:  a mass of fragments or particles loosely compacted together.

Sepideh Shahrokh, I try to answer your question with a view from some different angle:

surface tension also can be applied on solids; also solids have a surface tension, you can check the values in respective data bases. EVERY solid surface is covered by "something" (can be something like oil, or other stuff from the surrounding air, or - dependant upon the ature of the solid - water, usually monomolecular layer). By adsorption, some "interfacial tension" is created which is the difference between the 2 surface tension values.

If now 2 particles of the same nature agglomerate, 2 things happen:

- the adsorbed layer (let's say: the oil) is replaced by the other particle's surface

- on this contact POINT (almost no area!) the interfacial tension is Zero

As already mentioned above, the surface energy (and as well the interfacial energy) is the product of surface (or interfacial) tension times area. Therefore:

- for nanoparticles, agglomeration contributes a sigificant amount of "zero interfacial energy" area to the total interfacial energy - which these particles prefer to experience

- for bigger particles, their movement over-compensates the effect of the very few, insignificant amount of "zero interfacial energy" area.

Dear Bernhard  the surface tension (or interfacial tension), tension, and surface Energy, Gibbs and Helmholtz free energies are completely different thermodynamics quantities as clearly defined by Guggenheim for the layer theory in the case of isotropy, and they are also generalized for the elastic and hyperelastic  solids for the anisotropic surfaces and interfaces by Ogurtani et. al. (2005 and 2006). In the case of Gibbs model of surfaces where  h thickness is assumed to be zero, the difference in the surface Helmholtz and Gibbs specific free energies approaches to the surface tension asymptotically. (R. Defay,  I., Priggogine and A., Bellemans 1966, Surface tension and adsoption). 

It is very interesting, if the particle is fine, means the microscopic surface is not at all fine.  So, there are so many forces like electrostatic, Van der Waals bindig forces etc  have role on fine particle binding. As an example,  If two  grains are  oppositely charged electrostatic attraction may help for binding.  This result for the agglomeration.  The agglomeration is also a growth phenomenon, so the theoretical explanation also possible based on free energy concept.

 Herring essentially utilizes the Gibbs model of surfaces and puts strong emphasis on the definition of surface tension by Gibbs in terms of intensive variables, namely .  Where  A =[Fexcess -  SUMi Gamai ChemPoti ]   is the usual surface-tension.  Fexcess   is the specific (excess) Helmholtz free energy and Gama    is called the adsorption of species i  by Gibbs. Both quantities are defined with respect to the arbitrary selected dividing surface and therefore they are in general  abstract in character and their values are very sensitive to the precise choice of the position of dividing surface. Only in the single component system the dividing surface can be chosen so that   Gama =0.  Which yields  A =  Fexcess ( The surface tension becomes equal to the excess surface Helmholtz free energy). 

I'm interested! I have a lot to read and review. I'll be back with my "foot in mouth" :-)

Working on the centrifuges? :-)

The Nanoparticles possess large surface area as compared to its volume and so it behave differently from the bulk materials. Due to its large  ratio of  surface to volume , the physical, mechanical and electrical properties of the nanoparticles are considerably related to its surfactant. Therefore, in nano and sub-miron range, the particles have more tendency to agglomeration.

Enhanced surface to volume ratio in nanoparticles is the reason. 

Dear Rechard Padbury, your explanations is reasonable but there is some ambiguous points in some cases for me. As far as I know, the van der waals forces related to firts power of particle size. In an article ('The adhesion and removal of fine particles'), adhesion force was investigated for alumina powder particles with different particle size. It was showed that larger alumina particles have larger adhesion force.

 In addition, it is said that van der waals force is 10 times more than electrostatic (in short range).

Dear Bernhard Wessling, your response is really helpful. I think explanation about the surface area versus volume ratio of fine particles is a good reason for agglomeration of fine particles.  Furtheremore, that layer can reduce distances between particles or makes a capilary bridge so existance of this layer increases agglomeration of particles. My question is around why larger particles have more F(adhesion), while fine particles adhesion tendency is more than larger ones.

Peter, this sounds too generalistic to me (plus, I do not fully agree because "physical laws" and "material properties" exhibit different characteristic on each scale, atomic/molecular scale is different from nanoscale which is different from bulk scale. In some more simple words, for the nanoscale the most characteristic feature differentiating it from atomic/molecular and from bulk scale is the extremely high specific surface area, or in dispersion / emulsions, the extremely high interfacial area.

Peter, there is a very important principle in understanding of the behaviour of different levels of matter interaction, on which scale they interact - each scale generates new principles, new laws. Just as an example:

- living species (plants, animals including humans) consist of molecules which consist of elementary particles which consist of quarks (or whatever is there below)

- however, what we call "life" and "evolution" does not exist on the level of molecules / atoms / elementary particles.

Or even more simple: if you understand all the functions of tires, motors, gears, seats and any other component of a car (seat, doors, windows etc) - can you deduct from this the phenomenon of "traffic" or even more a "traffic jam"? - NO!

So, it is important to understand that every level of aggregation of matter generates its own *additional* laws how they interact, and the nanoscale is specifically characterized by (and the laws are based on) the fact that the nanoparticles exhibit an extremely high surface area, while

- bulk material has very low

- molecules, atoms have NONE! (not to talk about quarks) 

based on our studies, I think the main attraction force that it can dominate the gravity in the nano scale materials is a semi van der Walls force originated from debonded atoms at the surface.

Hi Sepideh. I had the same question. So I followed the thread. I learnt a lot but I didn't get answer to my main question. Now I am looking to the van der waals attraction equation: H=A.d/(24.a^2), where A is constant, d is the particle diameter and a is the distance between two particles, I guess the reason for higher agglomeration of smaller particles is that they are higher compact and the distance between particles are lower. This makes the denominator higher to the power of 2, which makes van de walls attraction higher in this case. Correct me if I am wrong.

The fine particles have much larger surface to volume ratio (for spherical geometry A/V= 3/R  compared to large particles.  THat means surface free energy versus bulk free energy is much higher. One can easily formulate the global Helmholtz free energy optimization, which includes not only the bulk but also the surface free energy.  That produces the critical size of the particle below which agglomeration should take place if there is a mechanical contact  occurs or they are embedded into a medium which allows matter transfer between particles by surface drift-diffusion. Actually this phenomena is closely related to the capillary forces, which involves the gradient of  (Kappa x Surface Helmholtz free energy density), where  Kappa is the local curvature. One can also formulate the general problem, which involves applied stress on the ensemble of particles using global Gibbs free energy. 

van der Waals attraction forces do not explain he phenomenon, because this would mean that the agglomeration forces are independant of the nature of the material which is not the case: the higher the surface tension, the stronger the adhesion forces; the agglomeration occurs because by agglomerating, the particles can reduce their surface energy because the now form an interface which has a lower interfacial energy than the pure isolated surface has; surface energy is surface tension times surface area, interfacial energy is the difference between the 2 surface tensions = Zero at the interface; that means, the more contact areas the particles can build, the more they can reduce their surface energy.

Dear Sepideh Shahrokh,

apparently the different professions are colliding here. Let me add the view of process engineers: It all boils down to the ration between contact forces and separating forces.

Pull off forces (for the same material, same shape, in the same environment) are usually greater for larger particles. At the same time pull of forces in a centrifuge would be even much greater for a bigger particle: bigger particles would therefore separate at a slower rotational speed. => there is no easy answer. For more see the attached link.

Yours,

Harald

http://www.mvt.ovgu.de/mvt_media/Vortr%C3%A4ge/mitps817.pdf

I am wondering what is the effect of relative humidity in the atmosphere. Can some one help me understand how does relative humidity affect agglomeration

that depends upon the surface tension of the agglomerating particles! if the surface tension is very low, then humidity will not affect because water will not adsorb on the particles.

Same, if the particles already have some oily stuff adsorbed in the surface.

So, one can not answer your question with just one simple phrase.