Polymer Physics Final

number average, weight average, viscosity average, z-average

four ways to calculate the average molecular weight of a polymer

different lengths and numbers of side branches

reasons that polymers have a distribution of molecular weights instead of one value

number average

in the general molecular weight formula was does k = 0 mean

weight average

in the general molecular weight formula was does k = 1 mean

z-average

in the general molecular weight formula was does k = 2 mean

viscosity average

which molecular weight average cannot be found using the general formula

Mk = (sum(NiMi^(k+1))/sum(NiMi^k)

general molecular weight form

number average molecular weight

the total weight of polymer divided by the total number of molecules

end group analysis, osmometry, ebullioscopy (boiling point evaluation)

three ways that number average molecular weight can be determined directly

weight average molecular weight

depends on the weight of the weight of the molecules as well as the number molecular weight

light scattering measurements

way that weight average molecular weight can be determined experimentally

polydispersity index (PDI)

measure of the distribution of molecular weights within a sample

>= 1

values of PDI

PDI = Mw/Mn

equation for PDI

the weights of all the molecules are the same

what does it mean if PDI = 1

combination of diffusion and sedimentary measurements

how can the z-average molecular weight be determined experimentally

the presence of high molecular weight chains

what is the z-average molecular weight sensitive to

dilute solution viscosity measurements

how is the viscosity average molecular weight determined experimentally

Mv = [sum(NiMi^(1+alpha)/sum(NiMi)]^(1/alpha)

equation for the viscosity average molecular weight

the shape of the molecule in the the solution

what does alpha represent in the viscosity average molecular weight equation

Mw=Mv

what happens when alpha = 1 in viscosity average molecular weight

Mz>Mm>Mv>Mn

for a typical polymer with alpha<1, rank the average molecular weights from largest to smallest

absolute, equivalent, relative

three characterizations for methods used to determine molecular weight in polymers.

measurement is directly related to molecular weight without assumptions

what makes a mw determining type absolute

the chemical structure of the polymer must be known to obtain molecular weight

what makes a mw determining method equivalent

a calibration curve relating measurement to molecular weight must be known

what makes a mw determining method relative

membrane osmometry, ebullioscopy, cryoscopy, analytical ultracentrifugation, static light scattering

five absolute mw determiners

end group analysis

equivalent mw determiner

solution viscosity, gel permeation chromotrography

relative mw determiners

10^4-10^6, Mn

membrane osmometry molecular weight values and mean value measured

<10^4, Mn

ebullioscopy molecular weight values and mean value measured

<10^4, Mn

cryoscopy molecular weight values and mean value measured

<10^5, Mn

end group analysis molecular weight values and mean value measured

10³-10^8, Mw, Mz

analytical ultracentrifugation molecular weight values and mean value measured

10²-10^8, Mw

static light scattering molecular weight values and mean value measured

10²-10^8, Mv

solution viscosity molecular weight values and mean value measured

10²-10^7, different values

gel permeation chromatography molecular weight values and mean value measured

colligative properties

properties of solutions that depend on the ratio of the number of solute molecules (polymer molecules) to the number of solvent molecules in a solution

freezing point depression, boiling point elevation, vapor pressure lowering, osmatic pressure

four types of colligative properties

lower

compared to pure solvent, freezing point is

higher

compared to pure solvents, boiling point is

lower

compared to pure solvent, vapor pressure is

reduced

compared to pure solvent, chemical potential is

molality of solute

freezing point depression and boiling point elevation are directly proportional to

mole fraction

vapor pressuring lower is directly proportional to

cryoscopy

freezing point lowering can also be called

(deltaTc/C)(C to zero) = (RTf^2)/rhodeltaHfMn + A2C

equation for freezing point depression

latent heat of fusion, density of the solvent, freezing point depression, freezing point of solvent

in the equation for freezing point depression what is deltaHf and rho and deltaTf and Tf

number of solute molecules dissolved per unit volume

what does freezing point depression depend on

ebulliometry

also called boiling point elevation

deltaTb, Tb, and deltaHv

what are the differences from the freezing point depression equation to boiling point elevation equation

latent heat of vapor

what is deltaHv in boiling point elevation equation

20000

for boiling point elevation the limitation of Mn is below

low observed temp differences for low concentrations of a polymer in molecular weight range of greater or equal to 20000 and lack of development of equipment

why are ebulliometric and cryoscopic measurements unattractive and less useful

4×10^-3 mmHg pressure

for polystyrene dissolved in benzene what is the vapor pressure depression

1.3×10^-3 deg C temp difference

for polystyrene dissolved in benzene what is the boiling point elevation

2.5×10^-3 deg C temp difference

for polystyrene dissolved in benzene what is the freezing point depression

1.5 cm height difference

for polystyrene dissolved in benzene what is the osmotic pressure

pi/c = RT(1/Mn + A2c + … )

what is the equation for real solutions for osmometer

gravity, difference in heights, solvent density, osmotic pressure

what is g, deltah, rho, and pi in the osmometer equation

second virial coefficient

what is A2

good solvent

what kind of solvent what A2 > 0

theta solvent

what kind of solvent when A2 = 0

poor solvent

what kind of solvent when A2 < 0

RT/Mn

what is the intercept

remains coiled and minimizes mixing

what happens when a poor solvent is used

maximizes mixing

what happens when a good solvent is used

polymers prepared by step polymerization since they have characteristic end groups

what kind of polymers is end group analysis suitable for

-OH and -COOH

what kind of end groups do polyesters have

-NH2 and -COOH

what kind of end groups do polyamides

ultracentrifugation

heavy and large particles settle at the bottom of the solution by process of sedimentation

frictional drag, buoyant force, gravitational force

what are the forces acting on a particle in ultracentrifugation

Ff = fu, frictional coefficient, velocity of particle

what is the equation for frictional drag and what are the variables in ultracentrifugation

Fs = m(omega^2r), mass, angular velocity, distance from the axis of rotation

what is the equation for gravitational/sedimentary force in ultracentrifugation

Fb = m0vbarr, mass of fluid displaced, specific volume, distance from axis of rotation

what is the equation and variables for buoyant force in ultracentrifugation

s = u/(omega^2r)

what is the equation for the sedimentation coefficient

the velocity of the particle per unit gravitational acceleration

what is the sedimentation coefficient

rate of spreading

what do you need to measure in ultracentrifugation to determine the diffusion coefficient

Mw = s/D(RT/(1-vbarrho))

what is the equation for weight average molecular weight from ultracentrifugation aka the svedberg equation

sedimentation coefficient and diffusion coefficient

what are the two coefficients that you need for molecular weight with ultracentrifugation

D = RT/Nf

what is the equation for diffusion coefficient ultracentrifugation

gel permeation chromatography, size exclusion chromatography, gel filtration chromatography

what are the types of chromatography used

molecular weight distribution

what is gel permeation chromatography (GPC) the only technique for characterizing

the strength and toughness of the polymer

as Mw/Mn decreases what increases

it becomes more difficult to process

as Mw/Mn decreases what happens negatively

pump, injector, columns, detector, data collection

what are the five stages of GPC

GPC

what is this the calibration for

the column set used

the calibration curve in GPC is characteristic to what

it separates on the basis of molecular size not molecular weight

what is the main limitation of GPC

identical molecular weights dissolved in suitable solvent

in GPC what is this illustrating

use both a viscometer detector along with a concentration detector

how do you avoid the convention GPC problem that it can only be used for a specific polymer that was used to find the calibration curve

property of isolated polymer coil solution as concentration tends to zero

intrinsic viscosity is

molecular density

intrinsic viscosity is inversely proportional to

eta = limctozero(etasp/c)

what is the huggins equation for intrinsic viscosity

eta = limctozero(lnetarel/c)

what is the kramer equation for intrinsic viscosity

huggins

which equation is used for the top line

kramer

which equation is used for the bottom line

volume/mass

intrinsic viscosity is proportional to

lower IV is a more compact structure therefore higher density

how does branching affect IV and why

density decreases so IV increases

how does increasing length affect IV