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PCC-20806 Soft Matter summary
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PCC-20806 Soft Matter summary. This summary contains all the topics from the PCC-20806 soft matter reader.
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InhoudChapter 1................................................................................................................................................1
Chapter 2................................................................................................................................................2
Chapter 3................................................................................................................................................4
Chapter 4................................................................................................................................................7
Chapter 5................................................................................................................................................9
Chapter 6..............................................................................................................................................12
Chapter 7..............................................................................................................................................15
Chapter 8..............................................................................................................................................18
Chapter 9..............................................................................................................................................22
Chapter 12............................................................................................................................................24
Chapter 10............................................................................................................................................27
Chapter 11............................................................................................................................................30
Chapter 1
Sof mater contann collonaal particle m polymmer m urfaactant aggregate or an per ea onl aroplet .
Theym have an nnhomogeneou tructure. Propertie ofa of materr
Mesoscopic length scale. Structural unnt that are much larger than atom .
Weak interactions. Weak non-covalent nnteraction nth an energym cale on the oraer ofa the
thermal energym. Thenr tructure n therefaore ea nlym aefaormea ana an ruptea.
Thermal flctlations. Sof mater ym tem are nn a con tant tate ofa ranaom (Bro nnan�
motion.
Self-assembly
Large response. Ea nlym nnfluencea bym external faorce or change nn conantion.
Slow response. The relativelym large length cale nn of mater lo ao n thenr aymnamnc .
Detanl are lumpea nnto efective nnteraction bet een the particle or polymmer m coarse-graining.
The of mater bunlanng block e nll con naer are collonaal particle m polymmer ana urfaactant .
Colloids are mall particle an per ea nn a fluna meanum. The anameter ofa the an per ea particle n
tympncallym bet een 1 nm ana 10 μm ana n much larger than the atomnc nze. Polymers are long chann-
lnke molecule maae ofa repeating chemncal unnt callea monomer . Slrfactants are a cla ofa
amphnphnlnc molecule m nth both a hymarophobnc part ana a hymarophnlnc part. Due to thenr amphnphnlnc
nature theym prefaer to nt at nnterfaace . When urfaactant are an olvea nn aterm the hymarophobnc
part ofa the molecule clu ter together.
,Chapter 2
2.1 Sedimentation
Collonaal an per non con n t ofa mall particle an per ea nn a fluna meanum. Ifa the particle have a
aen ntym that n anferent farom that ofa the meanumm theym expernence a net gravntational faorce. Thn net
faorce n equal to the anference bet een the gravntational faorce on the particle g ana the buoymancym
faorce b aue to the meanumr
F net=F g −F b=m 1− ( )
ρs
ρp
,
g=m g m’ n the apparent ma . or particle that are heavner than the
meanum ( ρ p > ρ s�m the net faorce n anrectea ao n ara ana the particle eanment. Ifa ρ p < ρ s the
particle move up ara m hnch n callea creamnng. A oon a the particle begnn to movem nt
expernence a farnction faorce fam hnch oppo e nt motion. Thn farnction faorce nncrea e a the velocntym
ofa the particle nncrea e m ana oon nt magnntuae equal the net arnvnng faorce re pon nble faor the
motion. Onnce the faorce acting on the particle balancem there n no faurther acceleration ana the
particle move nth a con tant velocntym.
F f =ζ v ζ n the farnction coefcnent (kg/ �.
Steaaym tate eanmentationm hen net= fa teaaym- tate eanmentation velocntym
m' g
v= The farnction faorce arn e becau e the (fluna� meanum ha to move pa t the particle a the
ζ
particle n movnng. or pherncal particle ofa raanu ar
ζ =6 π η aη n the vn co ntym (N m-2 or Pa �. Than the eanmentation velocntym ofa a pherncal particle n r
2a 2 ( ρ p −ρs ) g
v=
9η
2.2 Sedimentation equilibrium
A eanmenting ym tem n not nn equnlnbrnum. Afer ome time the eanmentea particle have
accumulatea to uch an extent that the proce come to a tana tillm eanmentation equnlnbrnum.
c (h ) −m ' gh
(Boltzman an trnbutionr =exp( )m c(h� ana c(0� are the equnlnbrnum concentration ofa
c (0 ) k BT
particle at henght h ana at henght h=0�
Average henght to hnch the particle can rn e a a re ult ofa thenr thermal motion (potential energym
equal thermal energym�r
kB T
h 0=
m' g
2.3 Ultracentrifugation
The eanmentation velocntym nn a centrnfaugal fela n r
dx m' ω 2 x
v= = ω n the angular velocntym (raa/ � ana x the an tance to the rotor axn .
dt ζ
2.4 Brownian motion
Particle unaergo an nnce antm chaotic motionm the Bro nnan motion. We kno that Bro nnan
motion n cau e bym the repeatea colln non bet een the collonaal particle ana the olvent molecule m
agntatea bym thenr thermal motion. The e colln non are ranaomm o that the total faorce acting on the
particle average out to zero on the long run. Ho everm at anym nn tant there maym be more colln non
on one nae ofa the particle than on the otherm ana the net faorce on the particle fluctuate con tantlym.
It n thn con tantlym fluctuating faorce that arnve Bro nnan motion (ranaom alk�. Snnce an placement
,to the rnght are equallym probable a an placement to the lefm the average an placement afer a gnven
time averagea over manym nnaepenaent trnal run m mu t be equal to zero.
Bro nnan motion n the arnvnng faorce faor anfu non.
¿ ∆ r 2 ( t )≥6 Dt Where ¿ ∆ r 2 ( t )> ¿ n the mean quare an placement ana D n the anfu non coefcnent
(m2/ �
kBT
D= Thn Enn tenn relation n quantitative ana unnver al; nt applne faor anym knna ana hape ofa
ζ
particle. or pherncal particle ofa raanu am e can ub titute the Stoke faormula faor the farnction
coefcnentm the Stoke -Enn tenn relationr
kB T
D=
6 π ηa
2.5 Interactions between molecules
The potential energym n relatea to the faorce bet een molecule a r
r
U ( r )=−∫ F ( r ' ) dr ' The faorce bet een the molecule can be obtannea farom the potential a r
∞
−dU
F (r )= The nnteraction potential n characternzea bym a trong repul non at verym hort an tance m
dr
hnch n ofen callea a ternc repul non (Pauln’ exclu non prnncnple�. At ome hat larger an tance m
there n an atractive contrnbution to the nnteraction potential. The atraction ha nt orngnn nn the
electro tatic faorce bet een the electron ana proton nn the molecule.
Intermolecular faorce r
Ionic interactions. The nnteraction energym bet een t o chargea molecule m or non m nth
q1 q2
charge q1 ana q2r U c ( r )= . ϵ 0=8.84x10-12 C V-1 m-1.
4 π ϵ0 ϵr r
Van der Waals interactions. Onccur al o bet een unchargea molecule . Theym nncluae anpolar
nnteraction ana Lonaon-an per non nnteraction (ranaom anpole that occur even nn apolar
molecule a a re ult ofa fluctuation . Such ranaom anpole nnauce a corre ponanng oppo nte
−β
anpole nn a nenghbournng moleculem leaanng to a net atraction�. U VdW =
r6
Hydrogen bonds.
Hydrophobic interactions. Molecule that cannot particnpate nn the 3D net ork ofa hymarogen
bona nn ater perturb the local tructure ofa the ater arouna themm ana gnve the ater
molecule fae er po nbnlntie to faorm hymarogen bona m leaanng to a aecrea e nn entropym. Thn
entropym aecrea e n reaucea hen the apolar molecule are brought clo er togetherm
re ulting nn an efective atraction bet een the e molecule .
2.6 Interactions versus thermal motions: equilibrium
The fnal tate ofa a ym tem n aetermnnea bym the trength ofa the atraction ( ε ¿ bet een the molecule
comparea to the thermal energym kBT. When ε ≪ k B T the atraction n too eak to keep the
molecule together ana thermal motion cau e the molecule to preaa out ana faorm a ga pha e.
When ε k B T m the molecule begnn to tick together ana conaen e nnto a lnquna pha e. or ε ≫ k B T m
the atraction n o trong that the molecule are lockea tightlym nnto a crym tal tructure.
2.7 Interactions between particles
The tympncal hape ofa the nnteraction potential bet een t o particle re emble the hape ofa the
, nnteraction potential bet een t o molecule (repul nve ana atractive contrnbution at hort ana
longer eparation an tance m re pectivelym�. or atom m the nnteraction potential n fxeam ana
aetermnnea bym the electronnc orbntal tructure. Thn mean that change nn tructure mu t be nnauce
bym changnng the temperature or the pre ure. or collonaal particle m ho everm the nnteraction
potential can be mannpulatea nn manym aym .
2.8 Timescales in soft matter
When a ym tem n ubjectea to a uaaen change nn conantion m nt nll tart to evolve to ara a ne
equnlnbrnum tatem corre ponanng to the e ne conantion . The tran ntion to thn ne equnlnbrnum
tate take ome time; thn time n callea the relaxation time τ . The tympncal relaxation time nn of
mater (larger particle � are much longer than tho e nn nmple molecular lnquna ana ga e .
Bro nnan time caler time neeaea faor a particle to move a an tance comparable to nt o n nzer
a3 η
τB≅ The tympncal aetachment time ofa particle can be e timatea u nng the Arrhennu equationr
kB T
ε
τ ≅ τ B exp ( )When ε ≫ k B T (large atraction trength�m the aetachment time become verym
kB T
large. A a re ult m thermoaymnamnc equnlnbrnum n not al aym reachea (particle cannot aetach to fna
a more faavourable po ntion�.
Chapter 3
Mo t of mater ym tem are mnxture ofa anferent component that arrange them elve nn complex
morphologne . Unaer tananng the tructure ofa of mater ym tem requnre unaer tananng ofa the
pha e behavnour ofa mnxture .
3.1 The Gibbs energy of mixing: regular solution theory
Ifa ∆ mix G< 0m then the Gnbb energym n lo erea bym mnxnng o that the equnlnbrnum tate n a molecularlym
mnxea olution. Ho everm nfa ∆ mix G> 0m the mnxnng n unfaavourablem becau e nt oula leaa to an
nncrea e ofa the Gnbb energym.
∆ mix G=∆ mix H−T ∆mix S∆ mix H re ult farom the an ruption ofa contact bet een molecule nn the
pure compouna ana the faormation ofa ne contact bet een the anferent molecule . ∆ mix S reflect
the nncrea ea number ofa po nble confguration nn the mnxture a comparea to the pure
component . Entropym ofa mnxnng per latce nte (n� (ø n the volume faraction�r
∆mix S
=−k B ¿ or mnxea compo ntion m ∆ mix S n po ntivem o that the confgurational entropym al aym
n
faavor mnxnng.
∆mix H z
=k B T χ ø A ø B met χ = 2 k T (2 ε AB−ε AA−ε BB ). z aenote the number ofa nenghbor that
n B
each latce nte ha m ana ε AB , ε AA , ε BB are the nnteraction enthalpne at contact faor ABm AA ana BB.
The parameter χ n the enthalpym changem nn unnt k B T m hen a molecule A n move farom an
envnronment ofa pure A nnto an envnronment ofa pure B. nn mo t ca e χ >0 m o that enthalpym faavor
pha e eparation.
∆mix G
gmix = =ø A ln ø A + ¿ ø B ln ø B + χ ø A ø B ¿gmnx n the anmen nonle Gnbb energym. A aouble
n kB T
mnnnmumm nn a curve ofa Gnbb energym agann t ø A faor everal value ofa χ m nnancate that the olution
nll tena to pha e eparate.
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