Solutions to Exercise 3-Amphiphilic Polymers, 1) The EHEC polymer is mainly hydrophilic, but it. contains randomly distributed hydrophobic

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1 Solutions to Exercise 3-Amphiphilic Polymers, KJM ) The EHEC polymer is mainly hydrophilic, but it contains randomly distributed hydrophobic microdomains. The hydrophobically modified analogue () sample consists of a mixture of C 12 and C 14 alkyl chains grafted to the polymer backbone. The spacer of the spacer-containing analogue (HM4-EHEC) is made of four ethylene oxide groups. This spacer displaces the hydrophobic tails from the polymer backbone (see the schematic illustration in the Figure). 1

2 2) The binding of a surfactant, especially an ionic surfactant, to a hydrophobically modified polymer usually leads to an enhancement of the network strength at moderate surfactant concentrations. Formation of transient network HM-EHEC solution without surfactant. HM-EHEC solution in the presence of low surfactant concentration. HM-EHEC solution in the presence of moderate surfactant concentration. HM-EHEC solution in the presence of high surfactant concentration (disruption of the network). i) In the semidilute regime, the hydrophobically modified polymer forms an associative network in the absence of surfactant. ii) In the presence of a low amount of surfactant, surfactant-induced hydrophobic clusters are formed. iii) At moderate surfactant concentrations, mixed micelles are formed, which serve as junction 2

3 zones in the cross-linking process of the network (strengthening of the network). iv) At high levels of surfactant addition, the hydrophobic micro domains are solubilized and the network is gradually disrupted. 3) Illustration of the cloud point behavior for the EHEC/SDS and HM-EHEC/SDS systems (1wt % and 25 oc). 100 EHEC/SDS HM-EHEC/SDS CP ( o C) Concentration of SDS (mmolal) The hydrophobically modified polymer is less water-soluble than the unmodified analogue. As a 3

4 result the cloud point of the former polymer is lower. The difference in cloud point behavior of the EHEC/SDS and HM-EHEC/SDS systems at low surfactant concentrations can probably be related to the difference in cac value (EHEC/SDS with cac=3-3.5 mmolal and HM-EHEC/SDS with binding of SDS to the polymer at very low concentrations). At higher surfactant concentrations the cloud point curves approach each other; the effect of hydrophobic modification disappears. 4) Illustration of the effect of surfactant addition on the complex viscosity and the time of intersection for the systems EHEC/SDS, /SDS, and HM4-EHEC/SDS. 4

5 η* (Pas) [η* - η* 0 ] / η* Concentration of SDS (mmolal) τ* (s) freq. = 0.5 Hz EHEC HM4-EHEC τ* = 1/freq. (G' = G'') Concentration of SDS (mmolal) i) The relative change of the complex dynamic viscosity (η'-η'0)/ η'0 (see the inset figure) reveals that the strongest enhancement of the viscosity with surfactant addition is found for HM4-EHEC (ca. 20).Due to the higher flexibility of HM4-EHEC, this facilitates an exposure of the hydrophobic groups to the surfactant. 5

6 ii) In the absence of surfactant, the degree of association is more pronounced for than for HM4- EHEC. This is probably due to higher flexibility of the latter polymer. It is easier for the hydrophobic tails to avoid each other. iii) At very high surfactant concentration, the hydrophobic effect disappears, no difference between the systems. The hydrophobic microdomains and tails are solubilized. Comparison of the time of intersection and the slow relaxation time from DLS. τ* (s) τ s (s) τ s EHEC HM4-EHEC τ* a) EHEC HM4-EHEC b) β EHEC HM4-EHEC Concentration of SDS (mmolal) 6

7 i) Although the slow relaxation times from DLS are considerably longer than the corresponding relaxation times from rheology (perturbation due to oscillation), the curves representing the longest relaxation times (rheology) exhibit the same profiles as the corresponding curves for the slow relaxation time from DLS. This behavioral concordance suggests that the slow relaxation from DLS is also associated with chain or cluster disengagement. ii) The minimum of the stretched exponent β (β=1-n) is located at the surfactant concentration where the polymer-surfactant interaction is strongest, i.e., optimum in coupling strength (Ngai model). iii) At higher levels of surfactant addition, β rises, i.e., the coupling strength decreases. 5) The effect of surfactant on the q-dependence of the slow mode. τ 1 q α s s τ -1 s (s-1 ) 10 3 a) α s = 2.5 ± α s EHEC HM4-EHEC 5 α s = 4.4 ± 0.3 α s = 6.0 ± 0.5 8x q (m -1 ) 3x10 7 b) 0 mmolal SDS 5 mmolal SDS 50 mmolal SDS 2/β α s 4 3 2/β EHEC HM4-EHEC Concentration of SDS (mmolal) 7

8 i) The strongest q-dependence of the slow mode is observed at the interaction peak (viscosity maximum). ii) The effect of surfactant concentration on the q-dependence of the slow inverse relaxation time is described qualitatively by the coupling model of Ngai (2/β). In this framework, the pronounced interaction peaks observed at moderate surfactant concentrations suggest enhanced coupling effects. 6) Light scattering is a powerful method to characterize structural changes of a polymer network. In the range qξ<1, we probe with DLS the dynamic correlation length and this is related to the mesh size of the network. 1 τ f c 2 = Dq " Blob"mod eld : = c kbt 6πηξ h 8

9 If we are in the range qξ>1, the length scale q-1 is related to local properties, and the scattered intensity depends strongly on the length scale. We can determine the fractal dimension: I( q) q d f a) ξ h (nm) 10 1 EHEC HM4-EHEC b) d f EHEC HM4-EHEC Concentration of SDS (mmolal) i) The decrease of the dynamic correlation length (mesh size) with increasing surfactant concentration suggests a more homogeneous and "tighter" network. ii) A close inspection of the ξh data for EHEC reveals a maximum at about the cac. iii) The increase of the fractal dimension as the amount of surfactant increases suggests a more tight network. iv) At low surfactant concentrations bundles are formed, and at higher surfactant concentrations they are disrupted and a more homogeneous network is evolved. 9

10 7) Semidilute acid solutions of unmodified and hydrophobically modified chitosan can be transformed to gels by increasing the polymer concentration. In the gelation process, we have contribution from both entanglements and hydrophobic associations. The gel point is determined from a plot of tan δ versus concentration at several frequencies. The gel-strength parameter (at the gel point): G = G /tan δ = S ω Γ(1-n) cos δ G ~ G ~ ωn Fractal dimension (Muthukumar): n = dd ( + 2 2df ) 2( d+ 2 d ) f Characteristic data for incipient Chitosan and HM-Chitosan gels. 10

11 hydrophobicity (mol %) c* = 1/[η] (wt %) Gel concentration (wt %) n S (Pas n ) d f The gel concentration decreases as the hydrophobicity of the polymer increases (contribution from both entanglements and hydrophobic interactions). The gel-strength parameter increases with decreasing hydrophobicity. This result suggests that cross-links induced by entanglements are stronger than those formed by hydrophobic associations. It seems that a more tight network is formed in the gel-network of the unmodified chitosan. 11

12 8) Increasing polymer concentration and hydrophobicity of chitosan, both promote enhanced associations, i.e., the slow relaxation time increases. If the association situation and the thermodynamic conditions are not affected by an increase in temperature, we may expect an increase in chain mobility, i.e., the slow relaxation time decreases. τ s T/η 0 (K s 2 m/kg) τ s T/η 0 (K s 2 m/kg) a) 10 6 c polymer = 0.5 wt % UM-chitosan HM-chitosan (2.5 mol %) HM-chitosan (5 mol %) Temperature ( o C) 10 6 b) T = 35 o C Concentration (wt %) 12

13 9) The results show that increasing polymer concentration and hydrophobicity, both strengthen the shear-thinning effect. η γ ( α 1 ) Viscosity (Pas) Viscosity (Pas) 10 4 Chitosan wt % wt % wt % 3.75 wt % HM-chitosan (5 mol %) wt % wt % wt % 2.25 wt % Shear rate (s -1 ) 0.50 wt % 1.50 wt % 2.25 wt % 3.25 wt % 0.10 wt % 0.20 wt % 0.25 wt % 0.30 wt % HM-chitosan (2.5 mol %) HM-chitosan (10 mol %) Shear rate (s -1 ) Table 2. Values of the characteristic exponent (α) describing the non-newtonian behavior of chitosan and the HM-chitosans. Hydrophobicity Polymer concentration α (mol %) (wt %)

14 10) The value of the cloud point in solutions of poly(oxyethylene)-containing diblock (DB) and triblock (TB) is affected by the hydrophobicity and the molecular weight of the polymer. C 17 O C O (PO E) 14 0 D iblo ck p olym er (D B ) M w = M w /M n= O O C 17 C O (P O E ) 140 IPD I (PO E ) 140 O C C 17 T rib lock po lym e r (T B) M w = M w /M n= 1.1 N C O O C N O Iso phorone diisocya nate (IPD I) 14

15 150 2Φ Cloud Point ( o C) PEG (M=8000)/water (S. Saeki et al. Polymer 17, 685 (1976)) Diblock (DB)/water Triblock (TB)/water 0 1Φ Concentration (wt %) i) The cloud point curve for DB is similar to that of the corresponding poly(ethylene glycol) sample (phase separation at elevated temperatures), but somewhat lower. This is probably due to the poorer thermodynamic conditions of the DB/water system, induced by the introduction of the hydrophobic tail and the effectively higher molecular weight caused by hydrophobic association. ii) The cloud point for TB, over an extended concentration regime, is located at much lower temperatures than DB, which is attributed to poorer thermodynamic conditions (incorporation of hydrophobic tails) and the formation of flower-like micelles connected by bridges (high effective molecular weight). iii) The effect of the connectivity results in negative contribution to the second virial coefficient that promotes phase separation. 15

16 Difference in association behavior between DB and TB polymers: The DB polymer has one sticker per chain, while the TB polymer has stickers on both ends of each chain. The DB polymer (mono-functionality) forms micelles that overlap (no connectivity) in the semidilute regime, while the TB polymer (difunctionality) promote the formation of flower-like micelles connected by bridges. The "flowers" show incipient overlap, but the connectivity is not fully developed. The bridges provide the connectivity of the system. 16

17 11) We can see that the concentration dependence of the zero-shear viscosity is more pronounced as the amount of TB polymer increases. The reason for this is that the TB polymer promote the formation of bridges (the connectivity is established) and we obtain an entangled network i) We may note (see the inset plot) that the concentration dependence of the zero-shear viscosity for the TB polymer is described by η c 5 (suggesting a θ-like behavior). Actually, for entangled solutions of polystyrene at θ-conditions, the same value of the power law exponent has been reported. This indicates that the bridges are very effective in forming an entangled network. 17

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