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Hello everyone, welcome to another lecture for Drug Delivery Principles in Engineering.
Today we are going to continue our discussion that we were having on Polymers. Again,
I just want to quickly remind you all that this drug delivery course will involve lots and
lots of different interdisciplinary things. So, what I am doing currently is basically
bringing you all up to par at what are the different areas and what do they mean for drug
delivery.
So, we initially talked about what is drug delivery, how is it is distributed, what is the
current methods. So, pharmacokinetics of the drug how the administered and then we
talked about pro drugs which are quite a lot present in the market, almost 10 percent of
the drugs are pro drugs. We then followed it up with what we would desire the current
drug delivery field to go in direction so, that the patients can have a much better quality
of life.
And to go further into that I am introducing some concepts of polymers which are a big
part of modern drug delivery fields at least in research and more and more products are
coming out in the market for that. So, right now what I am doing is I am building up
some of the basic concepts of polymers that will be required as we go along in the
course. So, probably in the next 3 or 4 classes we are going to go jump into the core of
the drug delivery fields and all of this will be required for that.
(Refer Slide Time: 01:51)
So, let us continue our discussion on polymers. So, what we learned in the last class we
talked about the ways for synthesis of the polymers and mainly we discussed about step
and chain polymerization, how this is done, what are the advantages and disadvantages
and all of that.
(Refer Slide Time: 02:09)
While we were in the last class this was the slide that we last left it at. So, talking about
the molecular weight and as I just said typically in a polymerization you will have an
average molecular weight, because the chains will be varying in terms of the molecular
weights each of them will have a different molecular weight. So, we quantify this thing
called average molecular weights. So, just now we are going to continue this discussion
on this molecular weight.
(Refer Slide Time: 02:36)
So, the average molecular weights in the traditional fields have been defined in several
ways, unfortunately this is the case with most of the drug delivery areas where you will
find that literature has several different ways to define somewhat the same information
that is being given.
So, we need to know all this because when you read papers, when you talk when you
read different literature on these you will find different terms being used. So, now, I am
going to explain what are the most common terms being used. So, one of them is the
number average molecular weight and this is defined as the sum of the mole fractions of
the molecule with different molecular weights.
So, if let us say I have 3 different types of chains with 3 different molecular weights in
different fractions. So, all I have to do is just multiply the fraction with the molecular
weight of these 3 chains and then add them up. So, essentially further let us say this can
be changed as if Ni represents the number of moles with mass Mi then the total average
molecular weight will be
Mn = ΣNiMi / ΣNi
So, note this is the arthmetic mean of the molar mass distribution NiMi is also same as
Wi which is essentially nothing, but the weight of the polymer having the mass Mi. So,
we can also write the Mn, the number average molecular weight as nothing,
Mn = Σwi / Σ(wi/Mi)
So, just an example so, let us says if I have a polymer sample containing 9 moles with
the molecular weight of 30,000 Daltons and 5 moles with a molecular weight of 50,000
Daltons.
Then in this case what will be the number average molecular weight.
Mn = {[9 mol x 30000 g/mol] + [5 mol x 50000 g/mol]} / (9+5) mol
= 37,000 g/mol
So, essentially we are using this formula so, mole here is nothing, but numbers. So, this
is here and then essentially you are dividing by the summation of the total moles which
is 9 plus 5, which will give you an average of one number average molecular weight of
37,000.
Let us say in a second example we have a sample of 9 grams of molecular weight of
30,000 and 5 grams of molecular weight of 50,000 in that case we will have essentially
we will use the bottom formula which is essentially derived from the first formula
Mn = (9 + 5) g / {[9g / 30,000 g/mol] + [5g / 50000 g/mol]} = 35,000 g/mol
(Refer Slide Time: 05:57)
Another one that is used is a weight average molecular weight and this is different from
the number average. This is defined as Mw is the summation of individual weights
multiplied by their total mass.
Mw = ΣWiMi
So, molar mass represents a weight fraction and these are the formulas given here this is
nothing, but a second order average of the total distribution. So, another example. very
similar example to what we had done last time, but this time we want to compute what is
the weight average molecular weight. So, we have 9 moles with molecular weight of
30,000 and 5 moles in the molecular weight of 50,000. In that case, all we have to do is
multiply the 9 mole with 30,000 square.
And then apply this formula and we will get 40,000, note this is very different from what
you got last time where you got close to about 37,000. So, it kinds of highlights that the
weight average molecular weight is different from the number average molecular weight
and again this can be represented in grams directly this is going to make the calculation
much simpler if you have grams there. So, essentially in this case you have to just
multiply the grams with the molecular weight and add them up and you get about 37,000.
So, as we said note that the Mw is typically always either greater or equal to Mn.
(Refer Slide Time: 07:28)
And this brings us to the polydispersity index which is a measure of the width of the
molecular weight distribution in a polymer sample. So, it is defined as a ratio between
the weight average molecular weight divided by the number average molecular weight.
PI = Mw / Mn
So, therefore, by definition if the polydispersity index has to be greater than or equal to 1
since we know that the Mw is always greater than or equal to the number average
molecular weight.
But if it is a perfectly monodispersed polymer only then you will have the Mw equal to
Mn and in that case the polydispersity index will be 1. So, greater the PI, broader is the
distribution of the weights. So, typically we want any polymers, we would like these
distribution to be narrow because that will help us identify what are the different
properties and how the polymers will behave. Higher the PI it is difficult to predict how
it is going to behave in terms of it is different properties.
So, as we can see here, in this case we see a fairly monodispersed polymer with a very
narrow distribution; however, the other case we see it quite a bit distribution. So, in this
case we can say that; obviously, the polydispersity for the 2 is much greater than
polydispersity for the 1 and it is of course, absolutely perfect we get a polydispersity of 1
which is a straight line in terms of the curves.
Where do you typically get this? So, typically in all synthetic reactions it is very difficult
to get this. But; however, biology systems are very good, typically the proteins that are
synthesized by the body are all extremely monodispersed. So, if you quantify any
proteins present in the cell in terms of their molecular weight you will get some sort of a
distribution which is with the PI of 1 and a straight line in this curve.
(Refer Slide Time: 09:27)
So, how do we measure these molecular weights, I mean; obviously, these were all
theoretical values, but how do we know what is the molecular weight of a sample that we
are given with. And so, there are a number of techniques to use this and different
techniques gives different results, some techniques may give number average molecular
weight, while some will give weight average molecular weight.
So, some of these techniques are listed here we are not going to go through all of them,
but some of the common ones that we are going to talk about is membrane osmometry,
light scattering, viscosity measurements, as well as GPC and mass-spec.
(Refer Slide Time: 10:03)
So, let us talk about membrane osmometry, this is a very widely used and this gives a
measure of the number average molecular weight. So, essentially it is a colligative
property and it is typically ideal for polymers in a wide polymer range wide molecular
weight range. So, from starting from all the way from 50,000 to millions of a molecular
weight. It is fairly simple here, all you do is you have 2 compartments which is separated
by a semi permeable membrane that will allow the solvents to move through but will
prevent polymer to move through and you can measure the height difference because
what will happen due to the osmotic pressure, the solvent will try to reach into the
polymer solution to essentially make sure that the osmotic pressure is not there; however,
as it further goes in here this is also a height difference so, that creates a reverse pressure
as well. So, at some point it stabilizes and you can fit it in the equation from van’t Hoff
equation we are not going to go into the derivation, but you can use the van’t Hoff
equation to essentially get a relationship between the height difference here and the
concentration of the polymer here.
And this essentially you can then extrapolate to find molecular weight. This intercept
here, if you put it in the equation is nothing, but RT divided by the number average
molecular weight and since you know R you know T at what temperature the experiment
was performed and this line you have experimentally plotted you can get the value of Mn
through this intercept value.
(Refer Slide Time: 11:45)
Then there are light scattering-based methods these are representative of the molecular
weight determination again these are number average molecular weight and what they
typically give you is also an hydrodynamic radius.
So, how big these polymer chains are and not in terms of the molecular weight itself, but
in terms of the actual diameter or hydrodynamic radius of them. Typically these
techniques work again between wide ranges from all the way from 10,000 to millions of
the molecular weight and again we are not go into the details of the electronics here.
But essentially, a sample is put in a laser it is hit on the sample at different angles and the
scattered signal is then used to amplify and see how much the polymer sample is
scattering and then once these equations are fitted and gives you an estimate of what is
the molecular weight that is being present in your initial tube.
(Refer Slide Time: 12:47)
We can also have viscosity measurements again these are widely used as well. This also
represents molar mass. Lot of manufactures will only actually specify intrinsic viscosity
and not the molecular weights and generally the relation here is the higher is the molar
mass, the higher is the viscosity. Here is a very simple experiment. You fill in solution
containing your polymer and you basically time it as to how long it takes from the level
to go from A to B and this a efflux time will basically can be used to then measure what
is the viscosity. So, more time it takes; that means, it is more viscous which essentially
also means that it has a higher molecular weight.
(Refer Slide Time: 13:35)
So, again going further into details here so, let us say if you use a pure solvent the efflux
time is t0, once you have the solvent containing a certain concentration c, let us say the
efflux time is tc. Then there are several types of viscosity that are mentioned, you can go
through these the one that is very widely used is the intrinsic viscosity which can then be
computed through this particular method by extrapolating it to the concentration 0 and
from the Mark-Houwink-Sakurada equation we know that the intrinsic viscosity is
related with M as intrinsic is equal to K multiplied by M to the power of a, where K and
a are again experimentally determined through several experiments.
[η] = KMa
(Refer Slide Time: 14:27)
And then another very widely used, a very powerful method is the gel permeation
chromatography also called size exclusion chromatography and what it is you take small
volume of your dilute polymer solution and you inject it into a column that is packed
with beads. These are porous gels typically with the diameter in ranges of angstrom and
what happens here is, you have a column which is packed with beads, which are porous.
So, these beads have small pores going through them. So, if the polymer is small enough
to enter these pores the polymer then goes through it. If I zoom into a bead, you have
these pores going through these beads and if the polymer is small enough it goes and
interacts into these channels and it has to traverse all the way down through these pores.
So, whereas, the big polymers will essentially just come and go right through from the
outside because they cannot enter these pores. So, what essentially happens is the larger
polymer molecules will start coming out first whereas, the smaller polymer molecules
will take lot more time because they have a lot more path to cover through these beads.
So, that essentially results in separation of these polymers. So, the first one to elute is the
largest molecular weight and then as time goes on smaller molecular weights come out.
So, you can then plot concentration against the elution volume, which will give you also
a qualitative indication of what is the distribution of these and not only that you can
actually then separate them out into different fractions to make sure that you can get
different molecular weight fractions. And then that will also result in narrowing of your
particular polymer distribution ok.
(Refer Slide Time: 16:24)
So, that is in terms the techniques for measuring the molecular weight, next we are going
to talk about the crystallinity which is again a very important property when we talk
about drug delivery.
So, when a polymer is slowly cooled from a melt state, it typically forms an ordered
structure, these are similar to crystals such polymers are called crystalline or they can be
semi crystalline. And polymers with the regular, compact structures and strong
intermolecular forces like hydrogen bonds or ionic interactions have a very high degree
of crystallinity. And essentially what it means is, as the polymer chains are getting
attracting more and mor they are coming closer and closer and packing very well and
that results in the polymer being highly crystalline.
So, as crystallinity increases the polymer becomes opaque, because the chains are very
close now and it does not allow the light to pass through, it causes scattering of the light
so, something like Teflon will look white because of this reason. And if you heat this
polymer up, what will happen is more and more heat energy will go into this polymer
sample and there will be temperature Tm which is called a melt transition temperature, at
which all the crystalline regions are melted and the crystallinity disappears.
So, as the degree of crystallinity increases so, if you have more and more intermolecular
interactions between the chain, the melt transition temperature also increases.
(Refer Slide Time: 17:54)
So, the crystallinity can have major effects on several properties, it will change the
mechanical properties because more crystalline it is the more compact these chains are.
So, increased stiffness and it will become less flexible. The diffusion rates will change,
because now these chains are very tightly packed. So, because they are so, tightly packed
it will be less permeable to allow diffusion of molecules through it.
The rate of hydrolysis will change, because now even the water will find it hard to go in
and break these interactions apart. So, the rate of hydrolysis will also become slower.
(Refer Slide Time: 18:34)
And then like crystallinity, there is also amorphousness and not all polymers exhibit
crystallinity. So, they are polymers that are amorphous so, some polymers does not really
form any order structure, even though you can cool them down from melt state and these
polymers are called amorphous polymers.
And they sometimes are also referred to as glassy polymers and they essentially lack any
kind of crystalline domains and that scatter light so, they are typically transparent. On
heating, amorphous polymers are transformed from a very hard glass which is a
transparent to a very soft, flexible, rubbery state which is just molten chains flowing
around.
And loss of this amorphous structure to more a rubbery flexible state is called glass
transition temperature. So, at this temperature it will go from hard glassy state to a much
more rubbery state. So, very similar to Tm, but this is more defined for amorphousness.
(Refer Slide Time: 19:37)
So, again how does this glass transition temperature affects properties. So, since the
motion of polymer chains will increase above Tg, because it is now become rubbery
above the glass transition temperature, you will have lot more motion lot more diffusion
through it. It will change lot of properties like heat capacity, density, permeability,
dielectric constants, they all chain very abruptly at Tg.
Polymers are typically brittle below Tg. So, good example is a rubber ball if you cool it
down with let us say with liquid nitrogen and try to throw it with the impact it will just
completely shatter where as, otherwise if it is above the Tg which is at room temperature
even if you throw the rubber ball down it is fairly elastic and it will not break.
So, depending on the usage, proper polymers can be chosen. So, let us say if you are
looking for breast implants you want those to be more rubbery, more elastic. So,
silicones are used which have extremely low Tg and Tm and so, they are always fluid at
the body temperature with 37 degree Celsius. And similarly polystyrene PMMA these
are glassy state at room temperature and so, they are hard if you heat them up above 100
degree Celsius, they are essentially much more fluidic.
So, chain mobility is again very critical for diffusion. So, below Tg the diffusion is much
much slower compared to above Tg.
(Refer Slide Time: 21:16)
These are ideal circumstances typically in the nature you would not find polymers which
are completely crystalline or completely amorphous, they typically exhibit both to a
certain extent. So, an example here is the polyethylene terephthalate, which essentially is
abbreviated as PET, and this has several crystalline domains depending on how it is
cooled.
So, you can have as much as from 0 percent to 55 percent crystallinity depending on how
this is being formed. So, if you cool it very quickly it will result in very amorphous
structure, if you give it some time in cooling, very slow cooling let us say half a degree
Celsius per hour or something like that. The chains will have enough time to come in
contact with each other, interact from strong interactions and result in crystalline
structure all the way up to 55 percent.
So, plastic beverage bottles are PET, so, do you what do you think are they crystalline or
are they amorphous? So, remember what did I tell you earlier regarding what happens to
the light scattering, in general how elastic and soft it becomes. So, yes since we know
that these plastic bottles are transparent they cannot be crystalline because crystalline
structures scatter light and do not let the light to pass through so, they will be more
opaque.
So, the plastic bottles as we know are transparent made of PET so, it has to be
amorphous, with a low degree of crystallinity. So, by cooling slowly you can get more
ordered crystalline domains. So, the same PET you can get with a high degree of
crystallinity which is then used in textile fibers and tire cords and the same one can also
be used in plastic bottles, the only difference is how fast they are cooled.
(Refer Slide Time: 23:24)
And then finally, how do you measure what is the Tg and Tm of a polymer sample that
you are given. So, this is regularly done using differential scanning calorimetry. And so,
what is done is, you have a reference pan and you have a sample pan with the polymer
and you measure how much heat is being given to each of those and figure out the Tg
and Tm on the basis of that.
So, as polymer undergoes transition due to heating so, essentially what will happen is,
the heat is flowing the temperature is increasing as more and more heat is flowing, at the
Tg, it will cause a lot more absorption of heat to essentially melt these chains. The heat
flow increases then it becomes constant again and then when it is close to Tm you need
further induction of heat so, that the polymer chains can then be separated from the
intermolecular forces, so it goes further up.
So, these transition points you can then determine for all the samples that you have and
that will give you an idea of Tg and Tm. A quick note here is what do you think is Tc?.
So, this we already discussed, but what is Tc? So, Tc is nothing, but because you are
slowly heating it up from the transition from here to here, this is a point where more and
more intermolecular chains are coming in contact. Here, the sample was cold and so,
these molecular chains had no interactions because they were solid, but at this point these
molecular chains can now move around, they become glassy and these can then interact
and essentially form crystalline structure which when further heat is given, then breaks
apart and essentially leads to the Tm temperature being reached. So, I am going to
explain this curve further this is not a trivial curve.
(Refer Slide Time: 25:36)
So, let us see. So, the heat capacity of a system is the amount of heat needed to raise it is
temperature by 1 degree Celsius. So, if the material is not changing heat capacity this
curve will look like a straight line right, because you are giving constant energy per
second and then the temperature will continue to increase by 1 degree Celsius at it is
particularly heat capacity. So, in an ideal circumstances, you should have a straight line
like this, typically metals show this.
(Refer Slide Time: 26:05)
However, we know that the heat capacity of the polymers is usually higher above the Tg
and so, that is why you see that initially it is a straight line. At Tg more heat is required,
so, it takes up more to basically melts it and then the resulting polymer is above Tg and
so, it has a higher heat capacity. So, that is why you need more this differential that you
get is because, now the temperature has changed its property, it is heat capacity as well.
And then the crystallization is an exothermic process so, now these chains are coming in
contact with each other and forming bonds it could be Van der Waal, it could be a
hydrogen bonds and this releases heat and because it releases heat it does not need any
external heat flow that we are giving. So, the external heat flow requirement comes
down, but once the chains have formed it goes back up. So, if we are still talking about
the same polymer with the same heat capacity so, it is still at the same level.
And now as you go along the melting of the polymer chains to break them apart you
need to give further energy, because earlier they had released energy now to give the
further energy to break them apart. Hence so, this needs to go up and by this time it
becomes completely mobile and you have constant heat flow required to raise the
temperature. So, I hope this is now clear as to how this works.
(Refer Slide Time: 27:29)
So, what are the different factors that affect Tg. So, molecular weight is one of the major
factors because in a polymer chain the end groups are the ones that are highly mobile and
see if you have low molecular weight for the same amount of polymer, you have lot
more polymer chains and so, they have lot more energy to move around and so, you will
have a lower Tg. But if you have a higher molecular weight these chains can entangle
and that will result in a higher Tg.
If you have bulky side groups that will hinder chain motion, if it hinders change motion
it will increase the Tg. So, if you have PMA what is this PMMA, PMMA is nothing, but
an extra methyl that is present on the PMA chains. So, which one of this will have the
higher Tg? It will be PMMA, because it is now having another CH3 that will hinder the
motion of this chain.
If you have a strong molecular attraction between them you will have a higher Tg,
because now they will tend to interact with each other and will essentially decrease the
motion. If you add diluents and plasticizer at the time of these polymer heating, this
increases free volume and thereby the chain mobility will increase. So, this is one of the
ways that you can lower the glass transition temperature of a particular polymer.
And generally if it is higher Tm, it basically means that that polymer will also have
higher Tg.
So, we will end right here and we will now in the future classes we will go more into
biomedical polymers. So, this is a general discussion we gave on what polymers are, now
we are going to specify into what is the properties for the biomedical polymers, bio
engineering polymers that we will use for drug delivery. So, see you next time.
Thank you.
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