bài giảng đại cương về polymer

1. Chất dẻo
a) Định nghĩa: chất dẻo là những vật liệu polime có tính dẻo, tức là có khả năng bị biến
dạng dưới tác dụng bên ngoài và giữ được biến dạng sau khi ngừng tác dụng.
b) Thành phần:
- Thành phần cơ bản: là 1 polyme nào đó. Ví dụ thành phần chính của êbônit là cao su,
của xenluloit là xenlulozơ nitrat, của bakelit là phenolfomanđehit.
- Chất hoá dẻo: để tăng tính dẻo cho polime, hạ nhiệt độ chảy và độ nhớt của polime. Ví
dụ đibutylphtalat,…
- Chất độn: để tiết kiệm nguyên liệu, tăng cường một số tính chất. Ví dụ amiăng để tăng
tính chịu nhiệt.
- Chất phụ: chất tạo màu, chất chống oxi hoá, chất gây mùi thơm.
c) Ưu điểm của chất dẻo:
- Nhẹ (d = 1,05 ¸ 1,5). Có loại xốp, rất nhẹ.
- Phần lớn bền về mặt cơ học, có thể thay thế kim loại.
- Nhiều chất dẻo bền về mặt cơ học.
- Cách nhiệt, cách điện, cách âm tốt.
- Nguyên liệu rẻ.
d) Giới thiệu một số chất dẻo.
- Polietilen (P.E) : Điều chế từ etilen lấy từ khí dầu mỏ, khí thiên nhiên, khí than đá.
Là chất rắn, hơi trong, không cho nước và khí thấm qua, cách nhiệt, cách điện tốt.
Dùng bọc dây điện, bao gói, chế tạo bóng thám không, làm thiết bị trong ngành sản xuất
hoá học, sơn tàu thuỷ.
- Polivinyl clorua (P.V.C)
Chất bột vô định hình, màu trắng, bền với dung dịch axit và kiềm.
Dùng chế da nhân tạo, vật liệu màng, vật liệu cách điện, sơn tổng hợp, áo mưa, đĩa hát…
- Polivinyl axetat (P.V.A)
Điều chế bằng cách : cho rồi trùng hợp.
Dùng để chế sơn, keo dán, da nhân tạo.
- Polimetyl acrilat
và polimetyl metacrilat
Điều chế bằng cách trùng hợp các este tương ứng.

Là những polime rắn, không màu, trong suốt.
Polimetyl acrilat dùng để sản xuất các màng, tấm, làm keo dán, làm da nhân tạo
Polimetyl metacrilat dùng làm thuỷ tinh hữu cơ.
- Polistiren
Dùng làm vật liệu cách điện. Polistiren dễ pha màu nên được dùng để sản xuất các đồ
dùng dân dụng như cúc áo, lươc…
- Nhựa bakelit:
Thành phần chính là phenolfomanđehit. Dùng làm vật liệu cách điện, chi tiết máy, đồ
dùng gia đình.
- Êbonit: là cao su rắn có tới 25 - 40% lưu huỳnh. Dùng làm chất cách điện.
- Têflon : rất bền nhiệt, không cháy, bền với các hoá chất. Dùng trong công nghiệp hoá
chất và kỹ thuật điện.
2. Cao su
Cao su là những vật liệu polime có tính đàn hồi, có ứng dụng rộng rãi trong đời sống và
trong kỹ thuật.
a) Cao su thiên nhiên: được chế hoá từ mủ cây cao su.
- Thành phần và cấu tạo: là sản phẩm trùng hợp isopren.
n từ 2000 đến 15000
- Mạch polime uốn khúc, cuộn lại như lò xo, do đó cao su có tính đàn hồi.
Cao su không thấm nước, không thấm không khí, tan trong xăng, benzen, sunfua cacbon.
- Lưu hoá cao su: Chế hoá cao su với lưu huỳnh để làm tăng những ưu điểm của cao su
như: không bị dính ở nhiệt độ cao, không bị dòn ở nhiệt độ thấp.
Lưu hoá nóng: Đung nóng cao su với lưu huỳnh.
Lưu hoá lạnh: Chế hoá cao su với dung dịch lưu huỳnh trong CS2.
Khi lưu hóa, nối đôi trong các phân tử cao su mở ra và tạo thành những cầu nối giữa các
mạch polime nhờ các nguyên tử lưu huỳnh, do đó hình thành mạng không gian làm cao
su bền cơ học hơn, đàn hồi hơn, khó tan trong dung môi hữu cơ hơn.
b) Cao su tổng hợp:
- Cao su butađien (hay cao su Buna)
Là sản phẩm trùng hợp butađien với xúc tác Na.

Cao su butađien kém đàn hồi so với cao su thiên nhiên nhưng chống bào mòn tốt hơn.
- Cao su isopren.
Có cấu tạo tương tự cao su thiên nhiên, là sản phẩm trùng hợp isopren với khoảng 3000.
- Cao su butađien - stiren
Có tính đàn hồi và độ bền cao:
- Cao su butađien - nitril: sản phẩm trùng hợp butađien và nitril của axit acrilic.
Do có nhóm C º N nên cao su này rất bền với dầu, mỡ và các dung môi không cực.
3. Tơ tổng hợp:
a) Phân loại tơ:
Tơ được phân thành:
- Tơ thiên nhiên: có nguồn gốc từ thực vật (bông, gai, đay…) và từ động vật (len, tơ
tằm…)
- Tơ hoá học: chia thành 2 loại.
+ Tơ nhân tạo: thu được từ các sản phẩm polime thiên nhiên có cấu trúc hỗn độn (chủ yếu
là xenlulozơ) và bằng cách chế tạo hoá học ta thu được tơ.
+ Tơ tổng hợp: thu được từ các polime tổng hợp.
b) Tơ tổng hợp:
- Tơ clorin: là sản phẩm clo hoá không hoàn toàn polivinyl clorua.
Hoà tan vào dung môi axeton sau đó ép cho dung dịch đi qua lỗ nhỏ vào bể nước, polime
kết tủa thành sợi tơ. Tơ clorin dùng để dệt thảm, vải dùng trong y học, kỹ thuât.
Tơ clorin rất bền về mặt hoá học, không cháy nhưng độ bền nhiệt không cao.
- Các loại tơ poliamit: là sản phẩm trùng ngưng các aminoaxit hoặc điaxit với điamin.
Trong chuỗi polime có nhiều nhóm amit - HN - CO - :
+ Tơ capron: là sản phẩm trùng hợp của caprolactam
+ Tơ enan: là sản phẩm trùng ngưng của axit enantoic
+ Tơ nilon (hay nilon): là sản phẩm trùng ngưng hai loại monome là hexametylđiamin
và axit ađipic
:
Các tơ poliamit có tính chất gần giống tơ thiên nhiên, có độ dai bền cao, mềm mại, nhưng
thường kém bền với nhiệt và axit, bazơ. Dùng dệt vải, làm lưới đánh cá, làm chỉ khâu.

- Tơ polieste: chế tạo từ polime loại polieste. Ví dụ polietylenglicol terephtalat.
Tơ lapsan rất bền cơ học, bền
An ion-exchange resin or ion-exchange polymer
[1]
is an insoluble matrix (or support
structure) normally in the form of small (1–2 mm diameter) beads, usually white or
yellowish, fabricated from an organic polymer substrate. The material has highly
developed structure of pores on the surface of which are sites with easily trapped and
released ions. The trapping of ions takes place only with simultaneous releasing of other
ions; thus the process is called ion-exchange. There are multiple different types of ion-
exchange resin which are fabricated to selectively prefer one or several different types of
ions.
Ion exchange resin beads
Ion-exchange resins are widely used in different separation, purification, and
decontamination processes. The most common examples are water softening and water
purification. In many cases ion-exchange resins were introduced in such processes as a
more flexible alternative to the use of natural or artificial zeolites.
Most typical ion-exchange resins are based on crosslinked polystyrene. The required
active groups can be introduced after polymerization, or substituted monomers can be
used. For example, the crosslinking is often achieved by adding 0.5-25% of
divinylbenzene to styrene at the polymerization process. Non-crosslinked polymers are
used only rarely because they are less stable. Crosslinking decreases ion- exchange
capacity of the resin and prolongs the time needed to accomplish the ion exchange
processes. Particle size also influences the resin parameters; smaller particles have larger
outer surface, but cause larger head loss in the column processes.
Besides being made as bead-shaped materials, ion exchange resins are produced as
membranes. The membranes are made of highly cross-linked ion exchange resins that
allow passage of ions, but not of water, are used for electrodialysis.
There are four main types differing in their functional groups:
• strongly acidic (typically, sulfonic acid groups, e.g. sodium polystyrene sulfonate

or polyAMPS)
• strongly basic, (quaternary amino groups, for example, trimethylammonium
groups, e.g. polyAPTAC)
• weakly acidic (mostly, carboxylic acid groups)
• weakly basic (primary, secondary, and/or ternary amino groups, e.g. polyethylene
amine)
There are also specialised types:
• chelating resins (iminodiacetic acid, thiourea, and many others)
Contents
[hide]
• 1 Uses
o 1.1 Water softening
o 1.2 Water purification
o 1.3 Production of high purity water
o 1.4 Ion-exchange in metal separation
o 1.5 Catalysis
o 1.6 Juice Purification
o 1.7 Sugar Manufacturing
o 1.8 Pharmaceuticals
• 2 See also
• 3 Notes
• 4 Sources
[edit] Uses
[edit] Water softening
Main article: Water softening
In this application, ion-exchange resins are used to replace the magnesium and calcium
ions found in hard water with sodium ions. When the resin is fresh, it contains sodium
ions at its active sites. When in contact with a solution containing magnesium and
calcium ions (but a low concentration of sodium ions), the magnesium and calcium ions
preferentially migrate out of solution to the active sites on the resin, being replaced in

solution by sodium ions. This process reaches equilibrium with a much lower
concentration of magnesium and calcium ions in solution than was started with.
The resin can be recharged by washing it with a solution containing a high concentration
of sodium ions (e.g. it has large amounts of common salt (NaCl) dissolved in it). The
calcium and magnesium ions migrate off the resin, being replaced by sodium ions from
the solution until a new equilibrium is reached.
This is the method of operation used in dishwashers that require the use of 'dishwasher
salt'. The salt is used to recharge an ion-exchange resin which itself is used to soften the
water so that limescale deposits are not left on the cooking and eating utensils being
washed.
[edit] Water purification
In this application, ion-exchange resins are used to remove poisonous (e.g. copper) and
heavy metal (e.g. lead or cadmium) ions from solution, replacing them with more
innocuous ions, such as sodium and potassium.
Few ion-exchange resins remove chlorine or organic contaminants from water - this is
usually done by using an activated charcoal filter mixed in with the resin. There are some
ion-exchange resins that do remove organic ions, such as MIEX (magnetic ion-exchange)
resins. Domestic water purification resin is not usually recharged - the resin is discarded
when it can no longer be used.
[edit] Production of high purity water
Water of highest purity is required for electronics, scientific experiments, production of
superconductors, and nuclear industry, among others. Such water is produced using ion-
exchange processes or combinations of membrane and ion-exchange methods. Cations
are replaced with hydrogen ions using cation-exchange resins; anions are replaced with
hydroxyls using anion-exchange resins. The hydrogen ions and hydroxyls recombine
producing water molecules. Thus, no ions remain in the produced water. The purification
process is usually performed in several steps with "mixed bed ion-exchange columns" at
the end of the technological chain.
[edit] Ion-exchange in metal separation
Ion-exchange processes are used to separate and purify metals, including separating

uranium from plutonium and other actinides, including thorium; and lanthanum,
neodymium, ytterbium, samarium, lutetium, from each other and the other lanthanides.
There are two series of rare earth metals, the lanthanides and the actinides, both of which
families all have very similar chemical and physical properties. Ion-exchange is the only
practical way to separate them in large quantities. This application was developed in the
1940's by Frank Spedding.
A very important case is the PUREX process (plutionium-uranium extraction process)
which is used to separate the plutonium and the uranium from the spent fuel products
from a nuclear reactor, and to be able to dispose of the waste products. Then, the
plutonium and uranium are available for making nuclear-energy materials, such as new
reactor fuel and nuclear weapons.
The ion-exchange process is also used to separate other sets of very similar chemical
elements, such as zirconium and hafnium, which incidentally is also very important for
the nuclear industry. Zirconium is practically transparent to free neutrons, used in
building reactors, but hafnium is a very strong absorber of neutrons, used in reactor
control rods.
[edit] Catalysis
In chemistry ion-exchange resins are known to catalyze organic reactions. See for
instance self-condensation.
[edit] Juice Purification
Ion-exchange resins are used in the manufacture of fruit juices such as orange juice where
they are used to remove bitter tasting components and so improve the flavor. This allows
poorer tasting fruit sources to be used for juice production.
[edit] Sugar Manufacturing
Ion-exchange resins are used in the manufacturing of sugar from various sources. They
are used to help convert one type of sugar into another type of sugar, and to decolorize
and purify sugar syrups.
[edit] Pharmaceuticals
Ion-exchange resins are used in the manufacturing of pharmaceuticals, not only for
catalyzing certain reactions but also for isolating and purifying pharmaceutical active

ingredients. Three ion-exchange resins, sodium polystyrene sulfonate, colestipol, and
cholestyramine, are used as active ingredients. Sodium polystyrene sulfonate is a strongly
acidic ion-exchange resin and is used to treat hyperkalemia. Colestipol is a weakly basic
ion-exchange resin and is used to treat hypercholesterolemia. Cholestyramine is a
strongly basic ion-exchange resin and is also used to treat hypercholesterolemia.
Colestipol and cholestyramine are known as bile acid sequestrants.
Ion-exchange resins are also used as excipients in pharmaceutical formulations such as
tablets, capsules, and suspensions. In these uses the ion-exchange resin can have several
different functions, including taste-masking, extended release, tablet disintegration, and
improving the chemical stability of the active ingredients.
[edit] See also
• Ion exchange
[edit] Notes
1. ^ IUPAC "strongly discourages" the use of the term 'ion-exchange resin' to refer to
an ion-exchange polymer, but it remains very common: International Union of Pure
and Applied Chemistry (2004), "Definitions of Terms Relating to Reactions of
Polymers and to Functional Polymeric Materials (IUPAC Recommendations
2003)", Pure Appl. Chem. 76 (4): 889–906,

[edit] Sources
•
•
• F. Helfferich, Ion Exchange, McGraw Hill, New York, 1962 (Bible of the
subject).
• Ion Exchangers (K. Dorfner, ed.), Walter de Gruyter, Berlin, 1991.
• C. E. Harland, Ion exchange: Theory and Practice, The Royal Society of
Chemistry, Cambridge, 1994.
• Ion exchange (D. Muraviev, V. Gorshkov, A. Warshawsky), M. Dekker, New
York, 2000.
• A. A. Zagorodni, Ion Exchange Materials: Properties and Applications, Elsevier,

Amsterdam, 2006.
Retrieved from " />Categories: Polymers | Water | Synthetic resins | Polyelectrolytes
Polymer Solutions
by Susana B. Grassino
The importance assigned to polymer solutions, a topic whose discussion has evolved
from a mere informative mention in textbooks to whole books exclusively devoted to
that subject, has become increasingly notorious.
The reasons are based on key factors. In the first place, the understanding of the
behavior and both physical and chemical properties of macromolecules has been
mainly sustained in studies carried out in solution, like for example the
determination of the relative molecular mass, made by viscometry or gel permeation
chromatography (GPC). On the other hand, since polymer solutions are highly
viscous even at low concentrations, their commercial application includes a wide
range of products, from paintings to processed foods.
Therefore, we can then consider polymer solutions as liquid mixtures made of long
macromolecular chains, and small, light molecules of solvent (Grosberg and
Khokhlov, 1997). This, by the way, is not a usual situation. The large size of this
chains implies the employ of certain theoretical models, which should take into
account, among other things, the numerous and diverse conformations that these
flexible structures may assume. This particularity is not consistent with a behavior
that could be regarded as an "ideal" behavior. In addition to these features, it is
easily understandable that the studies performed in the evaluation of the physical-
chemical properties of macromolecules are focused on dilute solutions, where the
chains are separated by long distances, and therefore the interaction between them
is reduced to a minimum. This is not taken for the sake of simplicity, but also
because the properties of dilute solutions are governed by the properties of the
individual macromolecules. In the case of concentrated solutions, the chains are
entangled each other, their interaction increases, and in such conditions, the system
is no longer suitable to evaluate the contribution of each macromolecule in
particular.

To learn more about Polymer Solutions, just click on any of the following links:
Summary
 What Is "Solubility" And What It Depends On
 How a Polymer Gets Dissolved
 Thermodynamic Considerations For Polymer Solubility
 How Polymers Behave In Dilute Solutions
 Statistical Parameters
 How Can You Measure The Statistic Parameters?
 References
Solubility and What it Depends On
Keywords
hydrogen bond
It should be pointed out that not all polymers can be dissolved, and even though
when they can, the dissolution process may take up to several days or weeks.
According to Rosen (1982), there is an assembly of general rules for polymer
solubility, based on experimental observations, from which interesting conclusions
can be obtained.
Thus, it is well known that the dissolution of polymers depends not only on their
physical properties, but also on their chemical structure, such as: polarity,
molecular weight, branching, crosslinking degree, and crystallinity. The general
principle that states like dissolves like is also appropriate in the case of polymers.
Thus, polar macromolecules like poly (acrylic acid), poly (acrylamide) and polyvinyl
alcohol, among others, are soluble in water. Conversely, nonpolar polymers or
polymer showing a low polarity such as polystyrene, poly(methyl methacrylate),
poly(vinyl chloride), and poly(isobutylene), are soluble in nonpolar solvents.
On the other hand, the molecular weight of polymers plays an important role in
their solubility. In a given solvent at a particular temperature, as molecular weight
increases, the solubility of a polymer decreases. This same behavior is also noticed
as crosslinking degree increases, since strongly crosslinked polymers will inhibit the
interaction between polymer chains and solvent molecules, preventing those

polymer chains from being transported into solution.
A similar situation occurs with crystalline macromolecules, although in such a case
the dissolution can be forced if an appropriate solvent is available, or warming the
polymer up to temperatures slightly below its crystalline melting point (T
m
). For
example, highly crystalline linear polyethylene (T
m
= 135ºC) can be dissolved in
several solvents above 100ºC. Nylon 6,6 (T
m
= 265ºC), a crystalline polymer which is
more polar than polyethylene, can be dissolved at room temperature in the presence
of solvents with enough ability to interact with its chains, through for example,
hydrogen bonding. Branched polymer chains generally increase solubility, although
the rate at which this solubility occurs, depends on the particular type of branching.
Chains containing long branches, cause dense entanglements making difficult the
penetration of solvent molecules. Therefore the rate of dissolution in these cases
becomes slower than if it was short branching, where the interaction between chains
is practically non-existent.
How a Polymer Gets Dissolved
Keywords
random coil, hydrodynamic volume
As said earlier, the dissolution of a polymer is generally a slow process, which can
take even several weeks, depending on the structure and the molecular weight of a
given polymer.
When a low molecular weight solute such as sucrose is added to water, the
dissolution process takes place immediately. The sugar molecules leave the crystal
lattice progressively, disperse in water, and form a solution.
But polymer molecules are rather different. They constitute long chains with a large

number of segments, forming tightly folded coils which are even entangled to each
other. Numerous cohesive and attractive both intra and intermolecular forces hold
these coils together, such a dispersion, dipole-dipole interaction, induction, and
hydrogen bonding (Figure 1a).
Based on these features, one may expect noticeable differences in the dissolution
behavior shown by polymers. Due to their size, coiled shape, and the attraction
forces between them, polymer molecules become dissolved quite slowly than low
molecular weight molecules. Billmeyer Jr. (1975) points out that there are two stages
involved in this process: in the first place, the polymer swelling, and next the
dissolution step itself.
When a polymer is added to a given solvent, attraction as well as dispersion forces
begin acting between its segments, according to their polarity, chemical
characteristics, and solubility parameter. If the polymer-solvent interactions are
higher than the polymer-polymer attraction forces, the chain segment start to
absorb solvent molecules, increasing the volume of the polymer matrix, and
loosening out from their coiled shape (Figure 1b). We say the segments are now
"solvated" instead of "aggregated", as they were in the solid state.
Figure 1. Schematic representation of the dissolution process for polymer molecules
The whole "solvation-unfolding-swelling" process takes a long time, and given it is
influenced only by the polymer-solvent interactions, stirring plays no role in this
case. However, it is desirable to start with fine powdered material, in order to
expose more of their area for polymer-solvent interactions.
When crystalline, hydrogen bonded or highly crosslinked substances are involved,
where polymer-polymer interactions are strong enough, the process does stop at this
first stage, giving a swollen gel as a result.
If on the contrary, the polymer-solvent interactions are still strongly enough, the
"solvation-unfolding-swelling" process will continue until all segments are solvated.
Thus, the whole loosen coil will diffuse out of the swollen polymer, dispersing into a
solution. At this stage, the disintegration of the swollen mass can be favored by

stirring, which increases the rate of dissolution.
However, once all the chain segments have been dispersed in the solvent phase, they
still retain their coiled conformation, yet they are now unfolded, fully solvated, and
with solvent molecules filling the empty space between the loosen segments. Hence,
the polymer coil, along with solvent molecules held within, adopts a spheric or
ellipsoid form, occupying a volume known as hydrodynamic volume of the polymer
coil (Figure 1c).
The particular behavior shown by polymer molecules, explains the high viscosity of
polymer solutions. Solvent and low molecular weight solutes have comparable
molecular size, and the solute does not swell when dissolving. Since molecular
mobility is not restricted, and therefore intermolecular friction does not increase
drastically, the viscosity of the solvent and the solution are similar. But the
molecular size of polymer solutes is much bigger than that of the solvent. In the
dissolution process such molecules swell appreciably, restricting their mobility, and
consequently the intermolecular friction increases. The solution in these cases,
becomes highly viscous.
Thermodynamic Considerations for
Polymer Solubility
Keywords
hydrogen bond, entropy
The evaluation of certain thermodynamic factors has allowed establishing if a
polymer in a given solvent will dissolve or not. Such factors are: the Gibbs free
energy (∆G) and the solubility parameters.
When a pure polymer is mixed with a pure solvent at a given temperature and
pressure, the free energy of mixing will be given by:
∆G = ∆H - T∆S
[1]
Being ∆H, the change in enthalpy of mixing, T the absolute temperature in the
process, and ∆S the change in entropy of mixing. According to equation [1], and
from the thermodynamic point of view, the dissolution will only take place if ∆G

sign is negative. ∆S is usually positive, since in solution, the molecules display a
more chaotic arrangement than in the solid state, and on the other hand, the
absolute temperature must be also positive. However, ∆H may be either positive or
negative. According to Rosen (1982), a positive ∆H indicates that both the polymer
and the solvent are in their lower energy state, whereas a negative value suggests the
solution is in its lower energy state, showing interactions such as hydrogen bonding,
which are established between polymer and solvent molecules.
When a polymer solution is formed, ∆S is significantly small. This contrasts the
found values when mixing masses or equivalent volumes of two low molecular
weight liquid substances. Qualitatively, this property can be explained by means of
a reticular model as shown in Figure 2.
Figure 2. Two-dimensional lattice model of solubility for a low molecular weight solute
To better understand this behavior, let’s assume that the black circles are solute
molecules, and the light blue circles are solvent molecules. When we are dealing
with low molecular weight solutes, their molecules can be distributed randomly
within the lattice, provided that two or more molecules do not occupy the same site
at the same time. Therefore, the configurational entropy of mixing, given by the
Boltzmann equation, is:
∆S = k ln W
[2]
where W the number of possible arrangements within the lattice, and k the
Boltzmann constant. With low molecular weight solutes, W is large, consequently
the entropy value will be high. Nevertheless, a different situation arises when the
solute molecules are part of a polymer. In such a case, these molecules must be
considered as a large number of segments of identical length, bonded each other
along a flexible chain.
At this point, how can we determine the possible arrangements within the lattice?
To find the answer, let's consider the solution concentrated enough so that the
chains are located randomly within the lattice, instead of forming isolated zones. If
we began with an end of the macromolecule, we will notice that there are eight

adjacent sites where the next segment can be placed.
Figure 3. Two-dimensional lattice model of solubility for a polymer solute
If the restriction that a site in the lattice cannot be occupied by two or more
molecules is maintained, the location of the third segment will fall in anyone of the
seven adjacent sites, and so on. The number of configurational possibilities will be
lower than that of the non-polymer molecules, because a restriction concerning the
distribution of the chains within the lattice has now been imposed. The term W in
equation [2] is then, smaller, and therefore the change in entropy is also smaller.
This reticular model was developed separately in the early 40s, by P.J. Flory and
M.L. Huggins. It explains the low entropy of mixing in polymer solutions.
Nevertheless, although this model was useful for an approximate calculation of the
term W, the theoretical Flory-Huggins model did not describe accurately the
behavior of real polymer molecules in solution, particularly, a dilute solution. For
that reason in 1950, Flory and Krigbaum developed a new model, taking into
account the properties of dilute solutions, which consist in alternate regions of pure
solvent and solvated polymer domains. The Flory-Krigbaum theory introduces two
important concepts, which will be discussed later: the
θ
temperature and the
excluded volume.
Now let's go back to the values of change in entropy for macromolecular solutions,
and the feasibility that a polymer can be dissolved in a given solvent. Since the term
T∆S in equation [1] is small, ∆H has to be small too. It must be even smaller than
T∆S in order to obtain a negative ∆G, and therefore, make the polymer be soluble.
For nonpolar macromolecules that do not have specific interactions with the solvent,
∆H is positive and has almost the same entalphy of mixing value to that for small
molecules. ∆H is given by a equation developed by Hildebrand:
∆H = φ
s
φ

p
(δ
s
- δ
p
)
2
[3]
Where φ
s
and φ
p
are the volume fractions of solvent and polymer, respectively,
whereas δ
s
and δ
p
represent the cohesive energy density (CED) for solvent and
polymer, respectively. This magnitude is a measure of the strength of the
intermolecular forces keeping the molecules together in the liquid state, and it is
known commonly with the name of solubility parameter. Its units are (cal/cm
3
)
1/2
, and
the equivalences to the SI units are the following:
(cal/cm
3
)
1/2

= (4.187 J/10
-6
m
3
)
1/2
= 2.046 x 10
3
(J/m
3
)
1/2
= 2.046 MPa
1/2

The solubility parameters are particularly useful when studying how capable is a
polymer to being dissolved in a given solvent. However, it should be pointed out that
equation [3] is valid only for solutions where strong polymer-solvent interactions do
not take place. Numerous tables showing solubility parameters for both solvent and
polymers have been published. Some examples are detailed below.
Solvent
δ
s
(MPa
1/2
)
Polymer
δ
p
(MPa

1/2
)
Acetone 20.3 Polybutadiene 14.6-17.6
Benzene 18.8 Polychloroprene 15.2-19.2
Carbon Tetrachloride 17.6 Polyethylene 15.8-18.0
Chloroform 19.0 Polyisobutylene 14.5-16.5
Cyclohexane 16.8 Polypropylene 18.9-19.2
Ethanol 26.0 Polyacrylonitrile 25.3-31.5
n-Hexane 14.9 Polymethylmethacrylate 18.4-26.3
Methanol 29.7 Polyvinyl acetate 18.0-19.1
Methylene Chloride 19.8 Polyvinyl alcohol 25.8
n-Pentane 14.3 Polyvinyl chloride 19.2-22.1
Toluene 18.2 Polystyrene 17.4-21.1
Water 47.9 Nylon 6.6 27.8
Table 1. Solubility parameters for solvents and polymers more commonly used. (Taken
from "Polymer Handbook" / J. Brandrup and E.H. Immergut, Eds., 3rd Ed., Wiley-
Interscience,
New York, 1989)
In absence of specific polymer-solvent interactions, it has been established that, for
a polymer to be dissolved in a given solvent, the term (δ
s
- δ
p
)
2
in equation [3], must
be smaller than 4.0. Thus, for example, according to the data shown in Table 1, if we
are trying to dissolve nylon 6.6 in water, we will see that it is not possible
thermodynamically, since (δ
water

- δ
nylon6.6
) = (47.9 - 27.8) MPa
1/2
= 20.1 MPa
1/2
>> 4.0.
However, nylon 6.6 will dissolve in toluene, since (δ
toluene
- δ
nylon6.6
) = (18.2 - 27.8)
MPa
1/2
= -9,5 MPa
1/2
<< 4.0. Making similar calculations, we will see that nylon 6.6
can also be dissolved in n-hexane and carbon tetrachloride.
It should be considered that the information the solubility parameters provide is
based on a thermodynamic rather than kinetic point of view. It means that if a
quick dissolution is what we are looking for, kinetically good solvents must be
employed. Usually, solvent mixtures of kinetically good liquids with
thermodynamically good liquids, assure a quick and efficient dissolution.
In polar systems or when polymer-solvent interactions occur, for example hydrogen
bonding, the calculation of the solubility parameters is carried out by means of
more complicated equations.
How Polymers Behave in Dilute Solutions
Until now we have seen the factors by which the solubility of macromolecules is
affected, from both physical, chemical and thermodynamic points of view. Now
what happens to these macromolecules when they are dissolved?

Due to their large number of carbon atoms bonded together forming a long chain,
polymers can generally adopt a lot of conformations. These conformations arise
from the numerous internal rotations that can occur through simple C-C bonds,
originating a number of rotational isomers.
Nevertheless, although the rotation of each bond is able to originate different
conformations, due to energy restrictions not all of them have the same probability
of occurrence. In such a case, the most stable conformations predominate in
solution, like proteins and nucleic acids, that is in biopolymers mainly.
However, synthetic polymers particularly, can display a large number of possible
conformations, and even though these conformations have not the same energy, the
differences are small enough so that the chains can change from one conformation
to another. This particularity gives a big flexibility to the macromolecules, and due
to this flexibility, the chains do not adopt a linear form in solution, but a very
characteristic conformation, known as random coil.
Figure 4. The random coil model
Such a flexibility can be understood more clearly with the help of molecular models,
as shown in Figure 5.
Figure 5. A C-C simple-bonded chain and its spacial representation. (Redrawn from
"Principles of Polymer Chemistry" / Paul J. Flory, Cornell University Press, Ithaca,
1953)
Let's assume C
1
, C
2
, and C
3
are carbon atoms in the same plane. According to this,
the atom C
4
can occupy any place throughout the circle, which represents the base

of a cone originated by the rotation of the bond E
3
. The angles of such bonds are
symbolized by ω, whereas the location of atom C
4
is specified by the internal angle
of rotation λ.
For a macromolecule in the solid state, the angle λ has a fixed value due to the
restrictions of the network packing. That is why the possible rotational isomers do
not occur. Nevertheless when this macromolecule is dissolved, the packing
disappears and the angle λ can vary widely, originating maximums and minimums
of energy. Thus, the probability of reaching diverse stable conformations with each
minimum of energy is high. On the other hand, the variation of the internal angle of
rotation is associated to an energy change that, at minimums, is small. Hence, the
chains can move freely to adopt such stable conformations. The fact that the chains
are changing from one conformation to another is also favored, due to the low
potential energy of the system. All these factors define, therefore, a flexible
macromolecule and from these concepts, the typical random coil form arises.
You might ask if the "shape" or magnitude of the random coil would remain the
same once the polymer has been dissolved. You will find that the answer is
absolutely negative and that the situation will depend not only on the kind of solvent
employed, but also on the temperature, and the molecular weight. The polymer-
solvent interactions play an important role in this case, and its magnitude, from a
thermodynamic point of view, will be given by the solvent quality. Thus, in a "good"
solvent, that is to say that one whose solubility parameter is similar to that of the
polymer, the attraction forces between chain segments are smaller than the
polymer-solvent interactions; the random coil adopts then, an unfolded
conformation. In a "poor" solvent, the polymer-solvent interactions are not favored,
and therefore attraction forces between chains predominate, hence the random coil
adopts a tight and contracted conformation.

In extremely "poor" solvents, polymer-solvent interactions are eliminated
thoroughly, and the random coil remains so contracted that eventually precipitates.
We say in this case, that the macromolecule is in the presence of a "non-solvent".
The particular behavior that a polymer displays in different solvents, allows the
employ of a useful purification method, known as fractional precipitation. For a
better understanding about how this process takes place, let’s imagine a polymer
dissolved in a "good" solvent. If a non-solvent is added to this solution, the
attractive forces between polymer segments will become higher than the polymer-
solvent interactions. At some point, before precipitation, an equilibrium will be
reached, in which ∆G = 0, and therefore ∆H = T∆S, where ∆S reaches its minimum
value. This point, where polymer-solvent and polymer-polymer interactions are of
the same magnitude, is known as
θ
state and depends on: the temperature, the
polymer-solvent system (where ∆H is mainly affected) and the molecular weight of
the polymer (where ∆S is mainly affected).
It may be inferred then, that lowering the temperature or the solvent quality, the
separation of the polymer in decreasing molecular weight fractions is obtained. Any
polymer can reach its θ state, either choosing the appropriate solvent (named θ
solvent) at constant temperature or adjusting the temperature (named
θ

temperature, or Flory temperature) in a given solvent. Table 2 compiles some values.
Polymer Solvent(s)
θ temperature
(
o
C)
Polyethylene n-Hexane 133
n-Hexanol / Xylene (70:30) 170

n-Octane 210
Polypropylene (atactic)
n-Butanol / Carbon Tetrachloride
(33:67)
25
n-Butanol / n-Hexane (32:68) 25
Cyclohexanone 92
Polystyrene Benzene / n-Butanol (58:42) 35
Cyclohexane 34-35
Cyclohexanol 79-87
Poly (vinyl acetate) Ethanol 19
Ethanol / Methanol (40:60) 36
Poly (vinyl alcohol) Ethanol / Water (41.5-58.5) 25
Water 97
Poly (vinyl chloride) Cyclohexanone 22
Dimethylformamide 36.5
Polyacrylamide Methanol / Water (2:3) 20
Polymethylmethacrylate Acetone -126
Cyclohexanol 77.6
Toluene -65
Dioxane / Water (85:15) 25
Table 2.
θ
solvents for selected polymers. (Taken from "Polymer Handbook" / J.
Brandrup and E.H. Immergut, Eds., 3rd Ed., Wiley-Interscience,
New York, 1989)
The θ temperature is a parameter arisen from Flory-Krigbaum theory. It is used to
calculate the free energy of mixing of a polymer solution in terms of the chemical
potentials of the species. We will further study the θ temperature relationship with
other important parameters that characterize dissolved polymers.

So far we have analyzed the influence of the solvent and the temperature in the
dimensions of the random coil. However is equally important to know what happens
to the viscosity of the macromolecular solution as the solvent becomes poorer.
Considering the chain molecules as rigid spheres, when a change from a "good"
solvent to a "poor" solvent takes place, the spheres become contracted. According
to the Einstein equation, the relative viscosity η
r
is obtained from:
[4]
That is to say, dividing the viscosity of the solution (η) by the viscosity of the solvent
(η
s
). From equation [4] it can be noticed that η
s
is directly proportional to the
volume fraction φ that these spheres occupy. Since, with the necessary
considerations, this reasoning can be transferred to macromolecules, which are not
rigid spheres, it may be inferred that if the segments are contracted in a "poor"
solvent, the viscosity of the solution will be smaller. Therefore, viscosity can be
adjusted according to the solvent quality.
Temperature, however, will not affect the viscosity of a polymer solution in a
relatively "poor" solvent. In this case, it should be considered that as the
temperature increases, the viscosity of the solvent (η
s
) decreases. However, on the
other hand, when the temperature is raised, a greater thermal energy will be
granted to molecules. Consequently, these molecules will tend to expand themselves,
increasing their volume fraction (φ). Thus both effects are compensated, and for this
reason the change of viscosity due to the increase of the temperature, is not
significant.

The measurement of viscosity in dilute macromolecular solutions has a fundamental
importance not only in the determination of molecular weights, but also, as we will
discuss later, in the evaluation of key parameters for the understanding of the
conformational characteristics of polymer solutions
Statistical Parameters
According to what we have been studying so far, dissolved polymer molecules do not
remain fully extended in a stationary state; instead they adopt a typical random coil
form in continuous motion, changing readily from one conformation to another.
When rotation around C-C simple bonds is hindered, the random coil conformation
is reached only at high temperatures, due to the thermal energy conferred to the
segments.
So you can ask the following question: it is possible to calculate the size of a
macromolecule in its typical random coil form, whose segments are constantly
changing from one conformation to another? The answer is affirmative, only if such
a size is expressed in terms of statistical parameters, which represent an average of
all the possible conformations. To that end, there are two very useful statistical
parameters:
End-to end distance
Represents the average distance between the first and the last segment of the
macromolecule, and ranges between a maximum value and a minimum value. The
maximum value appears when chains are fully extended, in a planar, zigzag
configuration known as "all-trans", where the contour length can be calculated
easily. The minimum value corresponds to the sum of Van der Waals radii in each
end.
Figure 6. Maximum value (left) and minimum value (right) for the end-to-end distance
r
The size of the macromolecule is given, in statistical terms, by the mean-square end-
to-end distance, 〈r〉
2
. Other authors express the root mean-square end-to-end

distance, that is to say, 〈r
2
〉
½
. The magnitude 〈r〉
2
is defined according to:
[5]
Where W is a probability distribution function.
The calculation of the mean-square end-to-end distance 〈r〉
2
, varies according to the
chain type, and the interactions that were taken into account.
Let's consider the simplest model of a polymer chain, i.e. an ideal polymer,
consisting of a series of N segments of length L. Let's assume that the chain
segments are bonded according to a linear sequence, without any restriction
regarding bonding angles ω and internal angles of rotation λ (Figure 5), so that the
atoms are separated each other at fixed distances but located in any direction. Thus,
the calculation of 〈r〉
2
can be made by means of a procedure known as random flight.