Structural analysis of PLP–SEC curves

PLP–SEC experiments to determine k^p were conducted in the concentration range from 5 wt% PEGMA in water up to bulk PEGMA

1 All PLP–SEC experiments were carried out by Stella Weber during her bachelor thesis.

10⁵ 10⁶ 10⁷

(B)

M / (g mol^1)

w(logM)

10⁵ 10⁶ 10⁷

w(logM)

M / (g mol^1)

(A)

d(w(logM))/d(logM)d(w(logM))/d(logM)

Figure 3.1: Molar mass distribution (solid lines) and associated first-derivate curves (dotted lines) for poly(PEGMA) samples from PLP experiments on aqueous solutions at 50 wt.% PEGMA, Darocur acting as initiator cini = 5 ∙ 10⁻² mol L⁻¹, νrep = 10 Hz, 30 °C (A) and bulk at cini = 5 ∙ 10⁻² mol L⁻¹, ν^rep = 15 Hz, 77 °C (B).

polymerization at temperatures from 22 to 77 °C. To match the PLP consistency criteria for reliable PLP–SEC experiments, initiator concentration and laser pulse repetition rate were varied. The number of applied laser pulses has been selected such as to keep monomer conversion below 10 % in order to keep monomer concentration almost constant and, on the other side, provide a sufficient amount of polymer for SEC analysis.

Shown in Figure 3.1 are typical MMD curves (solid lines) and associated first-derivate curves (dotted lines) obtained for poly(PEGMA) samples in aqueous solution and bulk PLP experiments at different reaction conditions. Depicted in Figure 3.1A is a PLP structure which is

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typical for experiments carried out between 22 and 40 °C in bulk and aqueous solution, and is close to the low-termination-rate-limit (LTRL).^[112] Above 40 °C, the PLP structure changes to the one presented in Figure 3.1B which corresponds to the intermediate-termination case.^[112] In both cases the resulting first-derivative curves show several pronounced maxima, whose positions correspond to the inflection points (POI) of the MMD.

The high-molar-mass material between 10⁶ and 10⁷ g ∙ mol⁻¹ without PLP structure results from continuous polymerization during and after the PLP experiment. However, the determination of kp is not affected by this high-molar-mass material as k^p has been deduced according to Equation 2.7 from POIs at significantly lower molar masses.

A selection of arithmetic mean kp values (complete Table see Appendix Table A2 to Table A5) deduced from the position of the POIs is listed in Table 3.1 together with all relevant experimental conditions, which are initiator concentration, cini, laser repetition rate, νrep, and monomer concentration in wt% and mol ∙ L⁻¹. The ratio of the molecular masses at the first and second POI plus the ratio of the second and third POIs, M¹/M² and M²/M³, respectively, is added to proof consistency and reproducibility of the measurement.

The occurrence of at least two POIs, with a multiple molecular mass of the first POI, is an important consistency criterion for reliable k^p determination via PLP–SEC.^[94,95] As can be seen from Table 3.1, the ratio of M1/M2 lies always above the expected value of 0.5 whereas the ratio of M2/M3 fulfills the expectations of 0.66. This behavior may be explained by the PLP structure. For the PLP structure close to the LTRL case, the molar mass of the first POI is estimated to be too high due to broadening and overlapping of each single signal in the MMD.^[79,113] In case of intermediate termination, the overlapping and broadening effects have only a minor influence on the POIs because of a better signal separation.^[113] The higher deviation at 10 and 5 wt% PEGMA may be caused by a low S/N ratio and monomer conversion up to 15 %.

Despite the inaccuracy of the first POI, the PLP structures provide up to six POIs. This high number of POIs allows for a particularly precise determination of kp. Shown in Figure 3.2 are the experimental kp

values reduced by the arithmetic mean k^p values plotted against the i-th inflection point from which k^p has been calculated. The k^p values

Table 3.1: Selection of measured k^p data in dependence on ν^rep, initiator and monomer concentrations at 22 °C. M¹/M² and M²/M³ represents the ratio of molecular weight at particular POIs (see Table A2 to Table A5 for complete table). The kp values are the arithmetic mean values of the second and higher POIs.

cPEGMA cPEGMA cInitiator νre

p M1/M2 M2/M3 kp

wt% mol ∙ L⁻¹ mol ∙ L⁻¹ Hz L ∙ mol⁻¹ ∙

s⁻¹

100 2.07 5∙10⁻² 20 0.54 0.67 521

40 0.57 0.68 583

70 0.60 0.72 715

5∙10⁻³ 20 0.55 0.67 494

70 1.40 5∙10⁻² 10 0.52 0.67 960

15 0.55 0.66 978

20 0.55 0.67 980

40 0.58 0.68 1100

5∙10⁻³ 20 0.56 0.64 907

50 0.96 5∙10⁻² 20 0.55 0.67 1397

40 0.57 0.67 1570

5∙10⁻³ 20 0.54 0.68 1414

30 0.58 5∙10⁻² 15 0.56 0.66 1579

20 0.56 0.68 1703

10 0.19 5∙10⁻² 15 0.58 0.72 2323

20 0.58 0.71 2700

5 0.10 5∙10⁻² 10 0.61 0.73 2890

15 0.62 0.71 3512

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Figure 3.2: Normalized k^p values deterimined from the i^th POI, i, of various PEGMA-H2O-compositions (PEGMA : H2O) at 22 °C. a.-c.: cini = 2 ∙ 10⁻² mol L⁻¹, ν^rep = 20 Hz. d.-e.: cⁱⁿⁱ = 2 ∙ 10⁻² mol L⁻¹, ν^rep = 15 Hz. f.: cⁱⁿⁱ = 2 ∙ 10⁻² mol L⁻¹, ν^rep = 10 Hz. The solid represent the arithmetic mean value of k^p from the second and higher POIs.

obtained from the first POI is always 10 to 20 % above the kp values derived from the higher POIs. The deduced kp values from the second and higher POIs are relatively constant and yield precise k^p values with a uncertainty of 5 %.

A further inaccuracy of kp has been reported for high νrep. With higher ν^rep, k^p increases because of the change in PLP structure toward the LTRL case and thus stronger overlap. To check for a dependency on νrep, the laser pulse repetition rate has been varied between 1 and 70 Hz.

As seen in Table 3.1 and Figure A3, kp increases with νrep higher than 20 Hz. This behavior is in agreement with findings by Beuermann,^[79]

and can be explained by the change of the PLP structure toward the LTRL.

The determined kp values have also been checked for independency of the initiator concentration to prove the consistency criterion, which is fulfilled in the investigated concentration range between 5 ∙ 10⁻¹ and 5 ∙ 10⁻² mol ∙ L⁻¹ (Figure A4).

Because of the above-described effects, arithmetic mean k^p-values have been determined from the second and higher inflection points with low νrep between 5 and 15 Hz, and initiator concentrations between 2 ∙ 10⁻² and 5 ∙ 10⁻² mol ∙ L⁻¹.