Diffusion Coefficients of Dyes in Hydrogels
Spring 2015
BE 191 - Lecture 7
1
In-Class Activity
Calculating Diffusion Coefficients of
Dyes in Hydrogels
Spring 2015
BE 191 - Lecture 7
2
Important Considerations
Understanding diffusion is key to designing controlled release systems and
fabricating engineered tissue constructs
Diffusion rates depend not only on the size of a molecule, but also many other
factors, including:
•
Molecular weight of diffusing species
•
Matrix mesh size
•
Temperature
•
Chemical/Structural properties of the diffusing species
•
Interactions between diffusing species and the matrix
Spring 2015
BE 191 - Lecture 7
3
Measure Dye Diffusion Coefficients
Split into teams, and receive the following from
the TFs:
•
4 hydrogel samples with dye
•
Two hydrogel samples were prepared at a
concentration, X and two at a
concentration, Y
Do the following:
1.
Determine whether Fick’s First or Second Law
applies to this case.
2.
Next, estimate the diffusion coefficients of
the dye molecules within each of these
hydrogels.
3.
Based on your results, which hydrogel
concentration X or Y is higher?
4.
If you wanted to achieve the same
diffusivities at a fixed hydrogel concentration,
what else could you change?
*Hashmark spacing on the tubes is 3.17 mm
t
Spring 2015
BE 191 - Lecture 7
4
Fick’s Second Law
x = 0
x = x
1
x = x
2
t = t
1
t = t
o
= 0
t = t
2
Concentrated dye,
C(x=0) = C
s
No dye in hydrogel,
C(x>0) = C
0
= 0
-
Concentration in
hydrogel,
C(x, t)
-
Assume
C
s
remains
constant for whole
experiment
-
1D diffusion problem,
assumes C
s
and C
0
are
constant and the gel is
infinitely long
Spring 2015
BE 191 - Lecture 7
5
Estimate Dye Diffusion Coefficients
Slope =
D
x
2
t
*Hashmark spacing on the tubes is 3.17 mm
A simple approach to estimate dye diffusivity in hydrogel matrices is to use:
D = L
2
/t
(units of cm
2
/sec)
Make this plot & determine the slope
for both cases!
What did you find?
Spring 2014
BE 191 - Lecture 1
6
Most agarose gels are between 0.7 - 2%
dissolved in a suitable electrophoresis buffer
The pore size of a 1% gel
~100 to 500 nm
DNA stained with ethidium bromide
Due to its negatively charged (phosphate backbone),
DNA towards the positively-charged anode
EtBr
Separating DNA by # of base pairs
Explore the calculation of diffusion coefficients of dyes in hydrogels based on factors like molecular weight, matrix mesh size, temperature, and chemical properties. Learn through in-class activities to determine the diffusion coefficients in different hydrogel concentrations, assess the applicability of Fick's laws, and consider key factors influencing diffusion rates for designing controlled release systems and tissue constructs.
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Presentation Transcript
Spring 2015 BE 191 - Lecture 7 1 In-Class Activity Calculating Diffusion Coefficients of Dyes in Hydrogels
Spring 2015 BE 191 - Lecture 7 2 Important Considerations Understanding diffusion is key to designing controlled release systems and fabricating engineered tissue constructs Diffusion rates depend not only on the size of a molecule, but also many other factors, including: Molecular weight of diffusing species Matrix mesh size Temperature Chemical/Structural properties of the diffusing species Interactions between diffusing species and the matrix
Spring 2015 BE 191 - Lecture 7 3 Measure Dye Diffusion Coefficients Split into teams, and receive the following from the TFs: 4 hydrogel samples with dye Two hydrogel samples were prepared at a concentration, X and two at a concentration, Y Concentrated? dye,? C(x=0)? =? Cs? x? =? 0? No? dye? in? hydrogel,? C(x>0)? =? C0?=? 0? x? =? x1? Do the following: 1. Determine whether Fick s First or Second Law applies to this case. 2. Next, estimate the diffusion coefficients of the dye molecules within each of these hydrogels. 3. Based on your results, which hydrogel concentration X or Y is higher? 4. If you wanted to achieve the same diffusivities at a fixed hydrogel concentration, what else could you change? x? =? x2? t? =? to? =? 0? t? =? t1? t? =? t2? *Hashmark spacing on the tubes is 3.17 mm t
Spring 2015 BE 191 - Lecture 7 4 Fick s Second Law x Concentrated dye, C(x=0) = Cs ( , ) C x t C erfc s 2 Dt - Concentration in hydrogel, C(x, t) x = 0 No dye in hydrogel, C(x>0) = C0 = 0 - Assume Cs remains constant for whole experiment x = x1 - 1D diffusion problem, assumes Cs and C0 are constant and the gel is infinitely long x = x2 t = to = 0 t = t1 t = t2
Spring 2015 BE 191 - Lecture 7 5 Estimate Dye Diffusion Coefficients Concentrated? dye,? C(x=0)? =? Cs? Make this plot & determine the slope for both cases! What did you find? x? =? 0? No? dye? in? hydrogel,? C(x>0)? =? C0?=? 0? x? =? x1? Slope = D x2 x? =? x2? t? =? to? =? 0? t? =? t1? t? =? t2? *Hashmark spacing on the tubes is 3.17 mm t A simple approach to estimate dye diffusivity in hydrogel matrices is to use: D = L2/t (units of cm2/sec)
Spring 2014 BE 191 - Lecture 1 6 Most agarose gels are between 0.7 - 2% dissolved in a suitable electrophoresis buffer Separating DNA by # of base pairs Due to its negatively charged (phosphate backbone), DNA towards the positively-charged anode EtBr The pore size of a 1% gel ~100 to 500 nm DNA stained with ethidium bromide
