I synthesized a nano composite based on guar gum. Later on, I studied the effect of cross linker concentration on % swelling and found out the value of optimized concentration of cross linker. At this optimized concentration the swelling percentage is about 1600 %. Far along using mathematical modeling, I tried to study the swelling behavior and get the value of diffusion constant in between 0 to 0.5 (normal diffusion).
My question is that:
In some articles in literature the swelling percentage is about 300 %. But the value of diffusion constant (n) lies in the range 0.5 to 1 means anomalous diffusion. Is It possible?
According to my understanding, in higher swelling sample diffusion of water is more into polymeric sample. Hence the values of diffusion constant are higher for higher swelling hydrogels as compare to lesser swelling hydro gels.
Thanks in Advanced.
Dear Mookkandi palsamy thanks for giving a valuable answer. I have an idea about what you have said, but my question is.
In some articles in literature the swelling percentage is about 300 %. But the value of diffusion constant (n) lies in the range 0.5 to 1 means anomalous diffusion. Is It possible?
Diffusion coefficient (D) is the amount of a particular solvent that diffuses across a unit area in unit time under the influence of a gradient of one unit. It is an important parameter indicative of the diffusion mobility. It was determined by following relation
D = π(h.θ / 4qeq)2
where qeq is swelling of gel at equilibrium, θ is the slop of the linear part of the swelling curves and h is the initial thickness of gel before swelling.
Note:
qeq = (Wh / Wd)
where Wh is the weight of swollen hydrogels at time t, and Wd is the initial weight of dry hydrogels.
Reference:
Mudassir, J. and N. M. Ranjha (2008). "Dynamic and equilibrium swelling studies: cross-linked pH sensitive methyl methacrylate-co-itaconic acid (MMA-co-IA) hydrogels." Journal of Polymer Research 15(3): 195-203.
Dear Mookkandi palsamy thanks for giving a valuable answer. I have an idea about what you have said, but my question is.
In some articles in literature the swelling percentage is about 300 %. But the value of diffusion constant (n) lies in the range 0.5 to 1 means anomalous diffusion. Is It possible?
The diffusion mechanisms of water into the
hydrogels and swelling capacity are affected by the concentrations of crosslinker and anionic comonomers. Some hydrogel which have high swelling capacity, the swelling constant (ks) is small while some of them have big ks values. Diffiusion coefficient (D) related with ks values. And generally D values increases with increasing ks valus. I think, you can find enough details in our work title of " Modeling of Swelling Behaviors of Acrylamide-Based Polymeric Hydrogels by Intelligent System " .
Jagdeep - check the Ph.D. thesis of C.K. Rhee Univ. of Wisconsin - Madison ~1978 - Rick Carpenter
Thin smear Diffusion - Radioactive Tagging
It is much more complicated in the BIOLOGICAL membranes and the CELL swelling, in short.
After equilibrium swelling amount of solvent uptaken by hydrogel is % swelling and diffusion coefficient is the proportionality factor D in Fick's law (see Diffusion) by which the mass of a substance dM diffusing in time dt through the surface dF normal to the diffusion direction is proportional to the concentration gradient grad c of this substance: dM = −D grad c dF dt. Hence, physically, the diffusion coefficient implies that the mass of the substance diffuses through a unit surface in a unit time at a concentration gradient of unity. The dimension of D in the SI system is a square meter per second.
Direct Methods:
Direct methods evaluate the diffusion coefficient by measuring concentration of the diffusing species (solvent) as a function of depth of penetration. Such methods are often more reliable and include the wide variety of physicochemical methods like mass spectrometry, radio-active tracer technique, spectrophotometry etc. The diffusivity is estimated by using compositional analysis techniques (Schmidt 1989). The drawbacks of direct methods are expense, time consumption and many of them are system-intrusive.
Indirect Methods:
Indirect methods measure the changes of one of the system parameters that depend on the diffusion rate. These parameters could be the rate of change of solution volume or movement of the gas-liquid interface, rate of pressure drop in a confined cell which is known as pressure decay method, rate of gas injection from the top to a cell in which the pressure and solution volume are kept constant, magnetic field characteristics, computed tomography (CT) analysis and dynamic pendant drop analysis. The advantage of these methods is that they do not need to determine the change in composition. In this section, the more common and modern methods will be introduced.
Swelling of hydrogels and swelling/shrinking biological of cells in unisotonic solutions are absolutely different games. Which one we are exactly talking about?
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