Synthesis and thermal studies of aliphatic polyurethane dendrimers: A geometric approach to the Flory-Fox equation for dendrimer glass transition temperature

Article abstract of DOI:10.1039/c1sm06725g

A new convergent synthesis for polyurethane dendrons to generation 4, and dendrimers to generation 3, is presented with control of surface functionality. The systematic synthesis of twenty-six new dendritic materials has led to a study of the factors affecting T_g using widely accepted approaches. The established understanding of dendritic polymer T_g behaviour is that the Flory-Fox models, used for linear polymers, are unsuitable as the high number of chain ends and globular nature of dendrimers requires special consideration. In our review of the accepted understanding we have shown that the conventional Flory-Fox models predict T_g∞ accurately and generate identical values to the established modifications of the Flory-Fox equation that consider 'dendrimer-relevant' aspects such as the non-zero values of n_e/M at infinite molecular weight. We also present a new approach using the geometric parameters of dendrimer mass evolution suggesting that the Flory-Fox equation is indeed appropriate for determination of dendrimer T _g∞.

Full text of DOI:10.1039/c1sm06725g

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PAPER
Synthesis and thermal studies of aliphatic polyurethane dendrimers:
a geometric approach to the Flory–Fox equation for dendrimer glass
transition temperature†
a
Alison Stoddart, W. James Feast and Steve P. Rannard
a
b
*
Received 12th September 2011, Accepted 7th November 2011
DOI: 10.1039/c1sm06725g
A new convergent synthesis for polyurethane dendrons to generation 4, and dendrimers to generation
3, is presented with control of surface functionality. The systematic synthesis of twenty-six new
dendritic materials has led to a study of the factors affecting Tg using widely accepted approaches. The
established understanding of dendritic polymer Tg behaviour is that the Flory–Fox models, used for
linear polymers, are unsuitable as the high number of chain ends and globular nature of dendrimers
requires special consideration. In our review of the accepted understanding we have shown that the
conventional Flory–Fox models predict TgN accurately and generate identical values to the established
modifications of the Flory–Fox equation that consider ‘dendrimer-relevant’ aspects such as the non-
zero values of ne/M at infinite molecular weight. We also present a new approach using the geometric
parameters of dendrimer mass evolution suggesting that the Flory–Fox equation is indeed appropriate
for determination of dendrimer TgN
.
Polyurethanes remain a particular class of dendrimer chemistry
that appears to be under-investigated. The effects of systematic
structural differences on glass transition temperature (Tg) within
this class of materials are also therefore not well reported.
Polyurethane dendrimers6a,b offer specific challenges during
synthesis as conventional functionality used to generate carba-
mates (isocyanates and alcohols) are difficult to stabilise during
the numerous reaction and purification steps required. A number
of approaches using protected functionality, e.g. masked isocy-
anates, have been reported that lead to predominantly aromatic
polyurethanes or dendrimers with mixed linking functionality eg
urea-urethanes.6c We have reported previously hyperbranched
polyurethane synthesis6d and a convergent route to aliphatic
polyurethane dendrimers which benefited from the selective
reactions of 1,10-carbonyl diimidazole derivatives and produced
dendrimers up to the third generation with N-tert-butox-
ycarbonyl surface functionality.6a
Introduction
Dendritic polymers1 offer different properties to conventional
linear polymers including encapsulation without prior self-
assembly, shape persistence, tunable behaviour via multiple end
group modification and, in the case of dendrimers, truly mono-
disperse molecular weight distributions.2 The range of ideal
dendrimer chemistries, synthesised by convergent or divergent
growth strategies,3 continues to grow and include polyesters,4a
polycarbonates,4b polyamidoamines,4c polyamides,4d,4e poly-
amines,4f glycopeptides,4g polyethers,4h carbosilanes,4i phospho-
rous-containing materials,4j triazines4k and organometallic4l
structures. The potential applications for dendrimers currently
under investigation also continues to increase with catalysts,5a
drug delivery/targeting,5b sensors,5c optical probes,5a solar cells
and light harvesting,5d contrast agents,5e gene delivery5f and
antimicrobials5g being among the most active areas.
The Tg of dendrimers has been studied experimentally and
using various modelling strategies. A recent report by Karatasos7
utilised molecular dynamics simulations of varying generations
of ideal dendrimer based on generalised AB2 repeat units. Local
intramolecular packing contributed significantly to the modelled
thermal behaviour with intermolecular factors, through inter-
penetration, appearing to have a lesser contribution, especially
with increasing generation. The study did not evaluate the effect
of different topological features, e.g. surface groups and spacer
length, or compare dendrons and dendrimers. Recent reviews8a
and articles8b,8c have reiterated that dendrimer Tg is affected by
end group substitution and correlated to a factor ne/M, which
aInterdisciplinary Research Centre in Polymer Science and Technology,
University of Durham, Durham, DH13LE, UK
bDepartment of Chemistry, University of Liverpool, Crown Street,
Liverpool, L69 7ZD, U.K. E-mail: srannard@liv.ac.uk; Fax: +44 151
794 3588; Tel: +44 151 3501
† Electronic Supplementary Information (ESI) available: Synthesis
details and structures for dendrimer and dendrons to generation 4;
comparative analysis of Tg using conventional Flory–Fox, modified
Flory–Fox and geometric progression equations for polyurethane
dendrons and dendrimers; example data for (ne/M)N determination;
detailed analysis of dendrons and dendrimers from ref.
9 using
conventional Flory–Fox, modified Flory–Fox and geometric
progression equations and demonstrating approaches to calculate
factors A, B and C. See DOI: 10.1039/c1sm06725g/
1096 | Soft Matter, 2012, 8, 1096–1108
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was first introduced by Wooley et al.9 as a modification of the
Flory–Fox equation10 to compensate for the increasing number
of end groups in dendrimer generations (where ne ¼ number of
polymer end groups; M ¼ molecular weight). Several reports
have shown that a more classical 1/M relationship is valid for
particular dendrimers. In general, it appears agreed that the
observed dendrimer Tg reaches a plateau at high generation.11a,11b
Herein we report the synthesis of a systematic range of poly-
urethane dendrons and dendrimers, from generation one to four,
with three different surface functionalities and two different core
molecules (aromatic and aliphatic). These twenty-six new mate-
rials have been investigated using differential scanning calorim-
etry (DSC) to establish trends in Tg and dendrimer structure.
Comparisons are presented that utilise the Flory–Fox equation
in its classical form and the generally accepted corrected equa-
tion that accounts for the unusual number of end groups inherent
in dendrimers, suggesting that the modified Flory–Fox equation
is unnecessary. We also derive a new and simplified equation
relating Tg purely to structural and repeating mass features of the
dendrimer and demonstrate that the accepted modifications of
the Flory–Fox equation relate directly to a classical 1/M rela-
tionship for Tg.
Two different MALDI-TOF mass spectrometers were used in
the characterisation of some of the macromolecules. Firstly,
a Kratos MALDI-IV MALDI-TOF mass spectrometer, and
secondly, a Voyager-DE STR MALDI-TOF mass spectrometer.
Trans-3-indole acrylic acid at a concentration in solution (THF)
of 10 mg mlꢀ1 was used as matrix for MALDI-IV experiments.
Dendritic polymer solutions of 1–3 mg mlꢀ1 were employed.
Dendritic polymer and matrix solutions were mixed in a ratio of
1 : 1 by volume and this solution was deposited into a well on the
slide. Mass spectra were obtained in linear mode using poly-
ethylene oxide (Polymer Labs) as an external calibrant. When
using the MALDI-TOF Voyager, trans-3-indole acrylic acid was
used as matrix at 10 mg mlꢀ1 in either THF or methanol
depending on dendritic polymer solubility. Dendritic polymer
solution concentrations varied from 1–3 mg mlꢀ1. Initially, the
matrix solution was deposited on the slide, followed by the
dendritic solution. Mass spectra were obtained in reflection mode
using polyethylene oxide (Polymer Labs) as external calibrants.
Some spectra were obtained in linear mode for comparison.
Analysis by GPC was achieved using tetrahydrofuran (THF)
as eluent using a flow rate of 1 ml minꢀ1 at 30 ꢁC. Columns
consisted of 2 ꢂ ‘mixed B’ columns containing PL-gel beads. The
columns were calibrated with polystyrene standards (Polymer
Laboratories) and samples analysed using conventional calibra-
tion with all data collected from a refractive index detector.
Differential scanning calorimetry (DSC) was conducted using
a Perkin Elmer Pyris 1 DSC calibrated using 99.9% cyclohexane
Experimental
Materials
Starting materials were purchased from Aldrich, Acros, Lan-
caster and Raylo Chemicals, Canada (CDI) and used without
further purification. Toluene and benzene were analytical grade
and were used as received. The ethanol used was general purpose
solvent grade. All reactions were performed under an atmo-
sphere of N2, unless stated otherwise. Silica gel used for column
ꢁ
and Indium metal. Samples wꢁere heated at a rate of 10 C per
ꢁ
ꢁ
minute from ꢀ180 C to 170 C, cooled at a rate of 50 C per
minute and ꢁheated a second time through the same temperature
range at 10 C per minute. Tg was measured as the midpoint of
the inflection of a plot of heat flow vs. temperature on the second
heating cycle. Melting points were obtained using an Electro-
thermal IA9200 series digital melting apparatus.
ꢀ
chromatography was supplied from Aldrich (70–270 mesh, 60 A)
ꢀ
or Fluorochem (40–63u, 60 A). For preparative gel permeation
chromatography, BioBeads ꢀ, S-X1 Beads purchased from Bio-
Rad were used in a column mode.
Typical synthesis of imidazole carboxylic esters of alcohols 4-
heptanol (1a), t-butanol (1b) and cyclohexanol (1c). In a round
bottom, glass flask with a reflux condenser attached, a solution of
1b (6.38 g, 86.1 mmol) in toluene (100 mL) was prepared at room
temperature. To this stirred solution was added CDI (16.7 g, 103.1
mmol) and the reaction mixture was heated at 60 ꢁC for 6 h. The
solvent was removed using a rotary evaporator and the oil
obtained redissolved in CH2Cl2 (200 ml). The organic phase was
washed with water (3 ꢂ 200 ml), dried over MgSO4, filtered and
the solvent removed in vacuo. The product was dried under
vacuum (10ꢀ1 mbar, 1 day), to yield the imidazole carboxylic ester
as a white crystalline solid (13.7 g, 95%). Found C 56.89; H 7.16; N
16.58%. Calculated for C8H12N2O2, C 57.13; H 7.19; N 16.66%.
13C NMR (62.9MHz, CDCl3) d (ppm) ¼ 27.6, 85.33, 116.9, 130.0,
136.8, 146.9. 1H NMR (300 MHz, CDCl3) d (ppm) ¼ 1.64 (s,9H),
7.07 (s,1H), 7.4 (s,1H), 8.13 (s,1H). Tm ¼ 51 ꢁC.
Methods
Elemental analysis data was obtained from an Exeter Analyser
CE-440. NMR spectra were recorded using either a Varian
Mercury-200 (1H at 200 MHz and 13C at 50.2 MHz), a Bruker
AM-250 (1H at 250.1 MHz and 13C at 62.9 MHz),
a
Varian Unity-300 (1H at 299.9 MHz and 13C at 75.4 MHz),
a Varian Mercury 400 (1H at 400 MHz and 13C at 100 MHz) or
a Varian Inova-500 (1H at 500 MHz and 13C at 125 MHz).
Deuterated solvents were used as supplied from Aldrich (CDCl3
and D2O) and Cambridge Isotope Laboratories (CD3OD and
(CD3)2SO). Chemical shifts (d) are reported in parts per million
(ppm) with respect to an internal reference of tetramethylsilane
(TMS) using residual solvent signals as secondary references.
For gas chromatography electron ionisation (GC-EI) and gas
chromatography chemical ionisation (GC-CI) were recorded
using Micromass Autospec instruments. Electrospray mass
spectra (ES- MS) were obtained on a Micromass LCT instru-
ment. A solution of the sample in dichloromethane of concen-
tration of 1 mg mlꢀ1 was diluted in methanol, to give a solution of
10 mg mlꢀ1. This solution was injected using a syringe pump at
Using 1c. Yield was a pale yellow oil (93%). Found C 62.49; H
8.60; N 13.23%. C11H18N2O2 requires, C 62.83; H 8.63; N
13.32%. 13C NMR (62.8 MHz, CDCl3) d (ppm) ¼ 13.0, 18.4, 36.0,
1
79.7, 117.1, 130.3, 137.0, 149.0. H NMR (300 MHz, CDCl3)
d (ppm) ¼ 0.95 (t, J ¼ 7.2 Hz,6H), 1.41 (m,4H), 1.69 (m,4H), 5.11
(qn, J ¼ 6.2 Hz,1H), 7.08 (m,1H), 7.43 (t, J ¼ 1.2 Hz,1H), 8.15
(s,1H). m/z (GC, EI) 210 [M + H]+, calc. Mw ¼ 210.27.
a flow rate of 10 ml minꢀ1
.
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Using 1a. Yield was a white crystalline solid (88%). Found C
61.83; H 7.33; N 14.32%. C10H14N2O2 requires, C 61.84; H 7.26;
N 14.42%. 13C NMR (62.9 MHz, CDCl3) d (ppm) ¼ 23.4, 25.0,
31.2, 77.7, 117.1, 130.0, 136.9, 147.9. 1H NMR (200 MHz,
CDCl3) d (ppm) ¼ 1.39–1.65 (m,6H), 1.79 (m,2H), 1.98 (m,2H),
5.01 (m,1H), 7.08 (s,1H), 7.44 (s,1H), 8.15 (s,1H). m/z (GC, EI)
194 [M + H]+, calc. Mw ¼ 194.23.
1.63 (s, br, OH), 2.34 (dd, J ¼ 12.9 Hz, J ¼ 9.9 Hz,1H), 2.46 (dd,
J ¼ 13.2 Hz, J ¼ 3 Hz,1H), 2.56 (dt, J ¼ 13.2 Hz, J ¼ 5.4 Hz,2H),
2.67 (m, 2H), 3.23 (m,4H), 3.73 (m,1H), 4.76 (qn, J ¼ 6 Hz,2H),
5.07 (s, br, O(CO)NHCH2). m/z (GC, EI) 446 [M + H]+, calc.
Mw ¼ 445.64.
Using 2c. 3c was a sticky colourless oil (86%). Tg ¼ 2.0 ꢁC.
Found C, 60.15; H 9.42; N, 9.67%. C21H39N3O5 requires,
C 60.99; H 9.51; N 10.16%. 13C NMR (62.9 MHz, CDCl3)
d (ppm) ¼ 19.8, 23.6, 25.2, 31.8, 39.2, 54.9, 63.1, 63.9, 72.7, 156.7.
1H NMR (300 MHz, CDCl3) d (ppm) ¼ 1.12 (d, J ¼ 6.4 Hz,3H),
1.25 (m,10H), 1.52 (m,2H), 1.72 (m,4H), 1.86 (m,4H), 2.33 (dd,
J ¼ 12.9 Hz, J ¼ 9.3 Hz,2H), 2.42 (dd, J ¼ 13.1 Hz, J ¼ 3 Hz,2H)
2.52 (dt, J ¼ 13.2 Hz, J ¼ 4.8 Hz,2H), 2.69 (m,2H), 3.22 (m,4H),
3.72 (m,1H), 4.62 (m,2H), 5.17 (s, br, O(CO)NHCH2). m/z (GC
CI) 414 [M + H]+, calc. Mw ¼ 413.55.
Typical selective synthesis of amine functional dendrons 2a, 2b,
2c. The imidazole carboxylic ester of 1a (33.0 g, 156.9 mmol) was
dissolved in toluene (250 ml) and diethylenetriamine (9.32 g, 90.3
mmol) added to the solution. The mixture was stirred and heated
at 60 ꢁC for 16 h. The solvent was removed under reduced pressure
and the mixture redissolved in CH2Cl2 (150 ml). The organic
phase was washed with distilled water (4 ꢂ 150 ml), dried over
MgSO4 and after filtration the solvent was removed in vacuo. The
colorless oil obtained was dried under vacuum (10ꢀ1 mbar) to give
2a as a white waxy solid (26.2 g, 86%). Found C 61.82; H 10.72; N
10.65%. C20H41N3O4 requires C 61.98; H 10.66; N 10.84%. 13C
NMR (100 MHz, CDCl3) d (ppm) ¼ 14.0, 18.5. 36.6, 40.6, 48.8,
74.4, 157.0. 1H NMR (400 MHz, CDCl3) d (ppm) ¼ 0.91 (t, J ¼ 7.2
Hz,12H), 1.40 (m,8H), 1.48 (m, 8H), 2.76 (t, J ¼ 5.2 Hz,4H), 3.27
(m,4H), 4.77 (qn, J ¼ 5.6 Hz,2H), 5.01 (s, br, O(CO)NHCH2). m/z
(GC, EI) 388 [M + H]+, calc. Mw ¼ 387.56.
Using 2b. 3b was a white crystalline solid (89%). Tg ¼ ꢀ18 ꢁC,
Tm ¼ 61.8 ꢁC (first heating run); Tg ¼ ꢀ5 ꢁC (second run). Found
C 56.21; H 9.82; N 11.57%. C17H35N3O5 requires, C 56.49; H
9.76; N 11.62%. 13C NMR (62.9 MHz, CDCl3) d (ppm) ¼ 20.0,
1
28.3, 38.7, 55.1, 63.0, 63.9, 79.3, 156.5. H NMR (300 MHz,
CDCl3) d (ppm) ¼ 1.12 (d, J ¼ 6.3 Hz,3H), 1.46 (s,18H), 2.37
(m,2H), 2.50 (dt, J ¼ 13.2 Hz, J ¼ 4.5 Hz,2H), 2.68 (m,2H), 3.19
(m,4H), 3.76 (m,1H), 5.13 (s, br, O(CO)NHCH2). m/z (GC, EI)
361 [M + H]+, calc. Mw ¼ 361.48.
Using the imidazole carboxylic ester of 1b. 2b was a white
crystalline solid (118.0 g, 77%). Found C 54.63; H 9.52; N
13.34%. Calculated for C14H29N3O4, C 55.42; H 9.63; N 13.85%.
13C NMR (62.9 MHz, CDCl3) d (ppm) ¼ 28.4, 40.3, 48.8, 79.7,
156.1. 1H NMR (300 MHz, CDCl3) d (ppm) ¼ 1.35 (s, br,
CH2NHCH2), 1.43 (s,18H), 2.71 (t, J ¼ 5.7 Hz,4H), 3.20 (m,4H),
4.99 (s, br, O(CO)NHCH2); on addition of a drop of D2O the
signals corresponding to the N–H resonances of the urethane and
secondary amine functions disappear. m/z (ES MS) 304
[M + H]+, 326 [M + Na]+, doubly charged adduct 629
Synthesis of 1-[N,N-bis(2-aminoethyl) amino]-2-propanol, 4.
4M HCl/EtOAc (250 mL) was added to a stirred solution of 3b
(55.0 g, 152.3 mmol) in EtOAc (100 ml) at room temperature. On
addition of the acid the reaction mixture effervesced and the
white suspension formed was stirred for 3 h. The mixture was
concentrated in vacuo and the orange oil obtained was dried
under vacuum to give the tris-ammonium salt of 4 as a pale
yellow solid. The tris-ammonium salt was characterized by
1H and 13C NMR spectroscopy; 13C NMR (62.9 MHz, D2O)
[2M + Na]+, calc. Mw ¼ 303.40. Tm ¼ 71 C.
ꢁ
1
d (ppm) ¼ 22.6, 36.5, 53.4, 62.7, 64.5 and H NMR (200MHz,
Using the imidazole carboxylicꢁester of 1c. 2c was as a white
crystalline solid (76%). Tm ¼ 58 C. Found C 60.32; H 9.37; N
11.71%. C18H33N3O4 requires, C 60.82; H 9.36; N 11.82%. 13C
NMR (100 MHz, CDCl3) d (ppm) ¼ 23.9, 25.3, 32.0, 40.5, 48.7,
D2O) d (ppm) ¼ 1.26 (d, J ¼ 6.4 Hz,3H), 3.21 (dd, J ¼ 13.6 Hz,
J ¼ 10.4 Hz,1H), 3.35 (dd, J ¼ 13.6 Hz, J ¼ 3 Hz,1H), 3.48
(m,4H), 3.62 (m,4H), 4.23 (m,1H). Amberlite ꢀ ion exchange
beads (700g) were activated by stirring the beads in a 2M KOH
solution in distilled water (300 mL) for 1 h. The beads were
subsequently isolated by filtration and washed with distilled
water (1000 ml). The tris-ammonium salt of 4 was dissolved in
distilled water (150 ml) and added to a beaker (1000 ml) con-
taining activated ion exchange beads in distilled water. The beads
and solution were stirred for 4 h and the mixture filtered. The
filtrate was concentrated using the rotary evaporator and the oil
obtained was stirred and dried under vacuum to give a pale
yellow solid. It was necessary to repeat the ion exchange process,
so after the reactivation of the beads the procedure was repeated
using the pale yellow solid. After this second ion exchange
process, a yellow oil was isolated. The oil was purified by vacuum
distillation (10ꢀ1 mbar, 160 ꢁC) to give 4 as a colourless oil (15.7
g, 64%). 13C NMR (62.9 MHz, CDCl3) d (ppm) ¼ 19.9, 39.8,
1
73.0, 156.5. H NMR (400 MHz, CDCl3) d (ppm) ¼ 1.23–1.56
(m, 12H), 1.71 (m,4H), 1.87 (m,4H), 2.76 (t, J ¼ 6 Hz,4H), 3.27
(m,4H), 4.63 (m,2H), 5.05 (s, br, O(CO)NHCH2). m/z (ES MS)
356 [M + H]+, 378 [M + Na]+, doubly charged adducts 711 [2M +
H]+, 733 [2M + Na]+, calc. Mw ¼ 355.47.
Typical synthesis of OH functional first generation dendrons 3a,
3b, 3c. To a stirred solution of 2a (26.2 g, 67.5 mmol) in ethanol
(200 ml), propylene oxide (11.8 g, 202 mmol) was added and the
mixture heated at 30 ꢁC for 20 h. Solvent was removed using the
rotary evaporator and the oil dried under vacuum (10ꢀ1 mbar,
1day). Purification by column chromatography (silica gel,
eluting with EtOAc) gave 3a as a colourless oil (23.8 g, 91%).
Tg ¼ ꢀ39.5 ꢁC. Found C 61.90; H 10.61; N 9.43%. C23H47N3O5
requires, C 61.99; H 10.63; N 9.43%. 13C NMR (62.9 MHz,
CDCl3) d (ppm) ¼ 14.0, 18.5, 20.0, 36.7, 39.2, 55.1, 63.2, 64.1,
74.4, 157.2. 1H NMR (300 MHz, CDCl3) d (ppm) ¼ 0.91 (t, J ¼
7.2 Hz,12H), 1.12 (d, J ¼ 6.3 Hz,3H), 1.33 (m,8H), 1.47 (m,8H),
1
57.8, 62.8, 64.8. H NMR (300MHz, CDCl3) d (ppm) ¼ 1.10
(d, J ¼ 6.3 Hz,3H), 2.32 (dd, J ¼ 13.2 Hz, J ¼ 9.9 Hz,1H), 2.44
(dd, J ¼ 13.2 Hz, J ¼ 2.7 Hz,1H), 2.58 (m,4H), 2.76 (m,4H), 3.79
(m,1H). m/z (GC, EI) 162.6 [M + H]+, calc. Mw ¼ 161.25.
1098 | Soft Matter, 2012, 8, 1096–1108
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Typical synthesis of OH functional second generation dendrons
5a, 5b, 5c. CDI (4.55 g, 28.1 mmol) was added to a stirred
solution of 3b (8.82 g, 24.4 mmol) in toluene (100 ml). The
MS) 1040.4 [M + H]+, 1062.4 [M + Na]+, 1078 [M + K]+, 521 [M +
H]2+, 532 [M + Na]2+, 539 [M + K]2+, 543 [M + 2Na]2+. m/z
(MALDI-TOF (Kratos) MS) 1041 [M + H]+, 1063 [M + Na]+,
1079 [M + K]+, calc. Mw ¼ 1040.34. GPC; Mw ¼ 970,
PDI ¼ 1.02.
ꢁ
mixture was heated at 60 C for 6 h. Subsequently, the reaction
1
mixture was analysed by H NMR spectroscopy and interpre-
tation of the spectrum indicated there was no evidence of the
starting materials. 4 (2.17 g, 13.4 mmol) was added and the
solution was heated for 20 h. The reaction mixture was concen-
trated in vacuo and redissolved in CH2Cl2 (200 ml). The organic
phase was subsequently washed with water (3 ꢂ 250 ml), dried
over MgSO4 and the solvent removed using a rotary evaporator.
The resulting pale yellow oil was purified by column chroma-
tography (silica gel, eluting with EtOAc:C6H12 3 : 2) and the
colourless oil obtained was dried under vacuum (10ꢀ1 mbar) to
give 5b as a colourless amorphous solid (5.7 g, 50%). Tg ¼ 25 ꢁC.
Found C 54.62; H 9.14; N 13.50%. C43H85N9O13 requires, C
55.17; H 9.15; N 13.47%. 13C NMR (400 MHz, CD3OD, 50 ꢁC)
d (ppm) ¼ 18.9, 21.0, 28.9, 39.9, 40.2, 55.7, 56.0, 61.1, 64.1, 66.2,
71.0, 80.1, 158.3, 158.8. 66.2 ppm is split into three peaks – 66.25,
Synthesis of third and fourth generation OH functional dendrons
6a, 6b, 6c, 7c. See electronic supporting information (ESI†).
Typical synthesis of first generation dendrimers with aliphatic
urethane cores. CDI (5.5 g, 33.9 mmol) was added to a stirred
solution of 3b (10.2 g, 28.3 mmol) in toluene (150 ml). The
ꢁ
mixture was heated at 60 C for 4 h. Subsequently, the reaction
1
mixture was analysed by H NMR spectroscopy and interpre-
tation of the spectrum indicated there was no evidence of the
starting materials. Tris(2-aminoethyl) amine (1.38 g, 9.42 mmol)
ꢁ
was added and the solution was heated at 60 C for 24 h. The
reaction mixture was concentrated in vacuo and redissolved in
CH2Cl2 (150 ml). The organic phase was subsequently washed
with water (3 ꢂ 150 ml), dried over MgSO4 and the solvent
removed by rotary evaporation. The crude product was purified
by column chromatography (silica gel, eluting with EtOAc:
C6H12, 1 : 1 increasing to EtOAc) to give G1-t-butyl-TAEA as
a colourless amorphous solid (3.7 g, 30%). Tg ¼ 38 ꢁC. Found C
55.72; H 8.96; N 13.37%. C60H117O18N13 requires, C 55.07; H
9.01; N 13.91%. 13C NMR (100 MHz, CD3OD at 50 ꢁC)
d (ppm) ¼ 19.0, 28.9, 39.7, 40.1, 55.2, 55.6, 61.0, 70.7, 79.8, 158.1,
1
66.18, 66.12 – with relative intensities 1: 2.0: 0.8. H NMR (500
MHz, CD3OD) d (ppm) ¼ 1.12 (d, J ¼ 6.0 Hz,3H, CH2CH(OH)
CH3), 1.19 (d, J ¼ 6.5 Hz,6H, C(H)(CH3)OC(O)N(H)), 1.40
(s,36H, C(O)C(CH3)), 2.41 (m,2H, NCH2CH(CH3)(OH)), 2.49
& 2.66 (m,4H, NCH2C(H)(CH3)OC(O)N(H)), 2.58 (m,12H, O
(CO)N(H)CH2CH2), 3.08 (m,12H, O(CO)N(H)CH2CH2), 3.22
(m,4H, O(CO) NHCH2CH2), 3.78 (m,1H, CH2CH(CH3)(OH)),
4.85 (m, obscured by H2O peak,2H, CH2C(H)(CH3)OC(O)N
(H)), 6.43 (s, br, O(CO)NHCH2), 6.88 (s, br,2H, O(CO)
NHCH2). m/z (ES MS) 936 [M + H]+, 958 [M + Na]+, 974 [M +
K]+, 469 [M + H]2+, 480 [M + Na]2+, 488 [M + K]2+, 491 [M +
2Na]2+, calc. Mw ¼ 936.19. GPC; Mw ¼ 1120, PDI ¼ 1.02.
158.5. 1H NMR (400 MHz, CD3OD)
d
(ppm)
¼
1.20
(d, J ¼ 6.4 Hz,9H), 1.44 (s,54H), 2.50 (dd, J ¼ 13.6 Hz, J ¼ 4.8
Hz, 3H), 2.57–2.63 (m, 21H), 3.04–3.25 (m,18H), 4.85 (m,3H)
6.43 (s, br, O(CO)NH CH2CH2), 6.79 (s, br, O(CO)
NHCH2CH2). m/z (TOF MS ES) 1307 [M + H]+, 1313 [M + Li]+,
1329 [M + Na]+, 676 [M + 2Na]2+. m/z (MALDI TOF (Kratos)
MS) 1307 [M + H]+, 1330 [M + Na]+, 1346 [M + K]+, calc. Mw ¼
1308.65. GPC; Mw ¼ 1780, PDI ¼ 1.01.
Using 3a. Purification was achieved by column chromatog-
raphy (silica gel, eluting with EtOAc:C6H12 1 : 2) to give 5a as
a sticky colourless oil (49%). Tg ¼ ꢀ4 ꢁC. Found C 59.54; H 9.91;
N 11.20%. C55H109N9O13 requires, C 59.81; H 9.95; N 11.41%.
13C NMR (62.9 MHz, CD3OD) d (ppm) ¼ 14.5, 18.9, 19.5, 20.9,
37.8, 39.9 (resonances from two distinct carbons overlap), 55.5,
55.9, 60.9, 64.0, 65.8 (split into 3 peaks), 70.6, 74.9, 158.6, 158.9.
1H NMR (400 MHz, CD3OD) d (ppm) ¼ 0.92 (t, J ¼ 7.2
Hz,24H), 1.12 (d, J ¼ 6.4 Hz,3H), 1.19 (d, J ¼ 6.4 Hz,6H), 1.30–
1.41 (m,16H), 1.47–1.54 (m,16H), 2.38–2.68 (m,18H), 3.09–3.28
(m,12H), 3.77 (m, 1H), 4.73 (m,4H), 4.85 (m,2H), 6.67 (s, br, O
(CO)NHCH2CH2), 6.89 (s, br, O(CO)NHCH2CH2). m/z (ES
MS) 1105 [M + H]+, 1127 [M + Na]+, 1143 [M + K]+, 553 [M +
H]2+, 564 [M + Na]2+, 575 [M + 2Na]2+. m/z (MALDI-TOF
Using 3a. The crude product was purified by column chro-
matography (silica gel, eluting with EtOAc:C6H12, 3 : 1
increasing to EtOAc) to give G1-heptyl-TAEA as a colourless
solid (32%). Tg ¼ 7 ꢁC. Found C 59.78; H 9.91; N 11.73%.
C78H153O18N13 requires, C 60.01; H 9.88; N 11.66%. 13C NMR
(62.9 MHz, CD3OD) d (ppm) ¼ 14.5, 19.0, 19.6, 37.9, 40.0, 55.3,
55.6, 61.0, 70.7, 75.2, 158.7, 159.2. 1H NMR (400 MHz, CD3OD)
d (ppm) ¼ 0.92 (t, J ¼ 7.2 Hz,36H), 1.20 (d, J ¼ 6 Hz,9H), 1.36
(m,24H), 1.50 (m,24H), 2.50–2.63 (m,24H), 3.10–3.21 (m, 18H),
4.73 (m,6H), 4.86 (m, obscured by H2O peak,3H), 6.66 (s, br, O
(CO)NHCH2CH2), 6.79 (s, br, O(CO)NHCH2CH2). m/z (ES
MS) 1561.1 [M + H]+, 1583.0 [M + Na]+, 781.3 [M + H]2+, 792.3
[M + Na]2+, 803.3 [M + 2Na]2+. m/z (MALDI TOF (Voyager)
MS) 1561.2 [M + H]+, 1583.1 [M + Na]+. m/z (MALDI TOF
(Kratos) MS) 1105 [M + H]+, 1127 [M + Na]+, calc. Mw
¼
1104.51. GPC; Mw ¼ 1180, PDI ¼ 1.01.
Using 3c. 5c was a colourless oil (42%). Tg ¼ 30 ꢁC. Found C
58.62; H 8.97; N 11.98%. C51H93N9O13 requires, C 58.88; H 9.01;
N 12.12%. 13C NMR (62.8 MHz, CD3OD) d (ppm) ¼ 18.9, 21.0,
24.8, 26.5, 33.1, 39.9 (resonances from two distinct carbons
overlap), 55.5, 55.9, 60.9, 64.0, 66.0 (split into 3 peaks), 70.7,
74.0, 158.6, 158.8. 1H NMR (400 MHz, CD3OD) d (ppm) ¼ 1.12
(d, J ¼ 6 Hz,3H), 1.18 (d, J ¼ 6 Hz,6H), 1.21–1.45 (m,20H), 1.56
(m, 4H), 1.74 (m,8H), 1.85 (m,8H), 2.40–2.70 (m,18H), 3.08–3.27
(m, 12H), 3.78 (m,1H), 4.56 (m,4H), 4.84 (m,2H), 6.61 (s, br, O
(CO)NHCH2CH2), 6.88 (s, br, O(CO)NHCH2CH2). m/z (ES
(Kratos) MS) 1557 [M + H]+, 1580 [M + Na]+, calc. Mw
¼
1561.13. GPC; Mw ¼ 1740, PDI ¼ 1.02.
Using 3c. The crude product was purified by column chro-
matography (silica gel, eluting with EtOAc increasing to EtOAc:
MeOH 100 : 5) to give G1-cyclohexyl-TAEA as a colourless
solid (32%). Tg ¼ 39 ꢁC. Found C 58.30; H 8.73; N 12.06%.
C72H129O18N13 requires, C 59.03; H 8.88; N 12.43%. 13C NMR
(62.9 MHz, CD3OD) d (ppm) ¼ 19.0, 24.9, 26.6, 33.2, 40.0, 55.3,
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55.5, 61.0, 70.8, 74.0, 158.7, 158.9. 1H NMR (400 MHz, CD3OD)
d (ppm) ¼ 1.19 (d, J ¼ 4.8 Hz,9H), 1.28–1.40 (m, 30H),
1.54 (m,6H), 1.75 (m,12H), 1.85 (m,12H), 2.49–2.61 (m, 24H),
3.16 (m,18H), 4.56 (m,6H), 4.85 (m, obscured by H2O peak,3H),
6.60 (s, br, O(CO)NHCH2CH2), 6.77 (s, br, O(CO)NH
CH2CH2). m/z (ES MS) 1464.8 [M + H]+, 1486.7 [M + Na]+,
732.9 [M/2 + H]+, 743.9 [M/2 + Na]+, 755.4 [M/2 + K]+. m/z
(MALDI TOF (Voyager) MS) 1464.9 [M + H]+, 1486.9
[M + Na]+, 1502.9 [M + K]+, calc. Mw ¼ 1464.87. GPC;
Mw ¼ 1350, PDI ¼ 1.02.
Synthesis of second and third generation dendrimers with
urethane and ester cores. See electronic supporting information
(ESI†).
Results and discussion
Synthesis
We have previously reported the synthesis of polyurethane
dendrimers using the selective reactions of 1,10-carbonyl diimi-
dazole derivatives.6a In summary, the strategy utilises either
a secondary or tertiary alcohol, 1, as the surface functionality for
a convergent dendrimer synthesis, Scheme 1. 4-Heptanol (1a),
t-butanol (1b) and cyclohexanol (1c) were chosen for the current
study to establish differences between highly flexible, sterically
bulky and cyclic aliphatic groups.
Typical synthesis of first generation dendrimers with aromatic
ester cores. A solution of 3b (2.0 g, 5.54 mmol) and 4-dimethy-
laminopyridine DMAP (1.8 g, 14.8 mmol) in benzene (100 ml)
was refluxed for 3 h with a Dean–Stark trap filled with molecular
sieves attached. The mixture was cooled to room temperature
and 1,3,5-benzenetricarbonyl trichloride (0.45g, 1.70 mmol) was
added. The reaction mixture was stirred and heated at 40 ꢁC for
3 h and then concentrated in vacuo. The crude product obtained
was purified by column chromatography (silica gel, eluting with
EtOAc:C6H12, 5 : 1) to give G1-t-butyl-BTT as a white amor-
Each alcohol was reacted with 1,10-carbonyldiimidazole (CDI)
to generate their imidazole carboxylic ester derivatives. Selective
reaction of the derivatives with diethylenetriamine led to the
formation of the di-urethane products, 2, without reaction at the
secondary amine functionality, as confirmed by mass spectrom-
1
etry and H and 13C nuclear magnetic resonance spectroscopy
ꢁ
phous solid (1.75 g, 83%). Tg ¼ 35 C. Found C 57.08; H 8.45;
N 9.86%. C60H105O18N9 requires, C 58.09; H 8.53; N 10.16%. 13
C
NMR (62.9 MHz, CDCl3) d (ppm) ¼ 18.1, 28.3, 38.3, 54.6, 59.2,
70.8, 78.9, 131.5, 134.3, 156.1, 164.4. 1H NMR (250 MHz,
CDCl3) d (ppm) ¼ 1.32–1.36 (m,63H), 2.58–2.79 (m,18H),
3.04–3.25 (m,12H), 5.18 (s, br, OC(O) NHCH2), 5.21 (m, 3H),
8.78 (s, 3H). m/z (MALDI TOF (Kratos) MS) 1240 [M + H]+,
1263 [M + Na]+, 1280 [M + K]+, calc. Mw ¼ 1240.53. GPC;
Mw ¼ 1320, PDI ¼ 1.01.
Using 3a. Crude product was purified by column chroma-
tography (silica gel, eluting with EtOAc:C6H12, 3 : 2) to give G1-
ꢁ
heptyl-BTT as a waxy white solid (75%). Tg ¼ ꢀ2 C. Found C
62.53; H 9.61; N 8.33%. C78H141O18N9 requires, C 62.75; H 9.52;
N 8.44%. 13C NMR (62.9 MHz, CD3OD) d (ppm) ¼ 14.5, 18.6,
19.6, 37.9, 39.9, 55.5, 60.7, 72.2, 75.2, 133.1, 135.3, 159.1, 165.7.
1H NMR (250 MHz, CD3OD) d (ppm) ¼ 0.90 (t, J ¼ 7 Hz,36H),
1.25–1.47 (m,57H), 2.65–2.91 (m,18H), 3.18 (m, 12H), 4.68
(m,6H), 5.23 (m,3H), 6.53 (s, br, OC(O)NHCH2), 8.83 (s,3H).
m/z (MALDI TOF (Kratos) MS) 1490 [M + H]+. m/z
(MALDI TOF (Voyager) MS) 1493.2 [M + H]+, 1515.2
[M + Na]+, 1531.0 [M + K]+, calc. Mw ¼ 1493.00. GPC;
Mw ¼ 1720, PDI ¼ 1.01.
Using 3c. The crude product was purified by column chro-
matography (silica gel, EtOAc:C6H12, 3 : 1) to give G1-cyclo-
hexyl-BTT as a white amorphous solid (78%). Tg ¼ 40 ꢁC. Found
C 61.67; H 8.42; N 8.87%. C72H117O18N9 requires, C 61.91; H
8.44; N 9.03%. 13C NMR (62.9 MHz, CDCl3) d (ppm) ¼ 18.1,
23.7, 25.3, 31.8, 38.6, 54.4, 59.2, 70.7, 72.7, 131.4, 134.3, 156.4,
1
164.4. H NMR (250 MHz, CDCl3) d (ppm) ¼ 1.29–1.39 (m,
39H), 1.53 (m,6H), 1.64 (m,12H), 1.82 (m,12H), 2.68–2.90 (m,
18H), 3.22 (m,12H), 4.58 (m,6H), 5.20 (s, br, OC(O)NHCH2),
5.26 (m,3H), 8.81 (s,3H). m/z (MALDI TOF (Voyager) MS)
1396.8 [M + H]+, 1418.8 [M + Na]+, 1434.8 [M + K]+. m/z
(MALDI TOF (Kratos) MS) 1395 [M + H]+, 1417 [M + Na]+,
1433 [M + K]+, calc. Mw ¼ 1396.75. GPC; Mw ¼ 1320,
PDI ¼ 1.01.
Scheme
1 Selective synthesis of polyurethane dendrimers using
1,10-carbonyl diimidazole (CDI) derivatives.
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(NMR). Ring opening of propylene oxide with 2 generated the
first generation dendrons, 3, bearing a secondary hydroxyl group
for subsequent reaction with CDI and formation of imidazole
carboxylic ester derivatives. 3b, derived from the initial reaction
of t-butanol, was also deprotected to form the triamino alcohol
AB2 branching unit 4. The imidazole carboxylic esters, from the
reaction of 3 with CDI, were reacted with 4 to form larger den-
drons. Repetition of this iterative synthesis led to a series of
dendrons, shown schematically in Fig. 1.
The generation 1–3 dendrons were coupled, using CDI
chemistry, with either tris(2-aminoethyl)amine (TAEA), to form
the polyurethane homodendrimer series, or directly with
1,3,5-benzene tricarbonyl trichloride (BTT), forming an
aromatic ester core and generating core variability within the
series of materials, shown schematically in Fig. 2.
Monitoring of the individual stages of dendron and dendrimer
synthesis by 1H and 13C NMR is often hampered at higher
generations due to overlapping signals and the inherent struc-
tural complexity. The polyurethane materials of this study have
an increasing number of chiral carbons generated during the ring
opening of propylene oxide. The chiral centres lead to modified
chemical environments at the diastereotopic methylene adjacent
to the tertiary amine. For the generation 1 dendrons the ineq-
1
uivalence of the methylene protons was readily seen in the H
NMR spectra as two doublet of doublets due to the germinal and
vicinal couplings, exemplified in Fig. 3A and 3B for the 4-heptyl
functional generation 1 dendron. The diastereotopic methylene
protons of the t-butyl functional dendrons were less resolved
than the cyclohexyl or 4-heptyl functional materials.
Fig. 2 Generation 3 4-heptyl and cyclohexyl functional polyurethane
dendrimers coupled with either (A) tris(2-aminoethyl)amine or (B)
1,3,5-benzene tricarbonyl tichloride cores and schematic representations
of the dendrimers.
At generation 2, the dendrons also exhibited a noticeable
difference with respect to the shift of the methyl protons in the 1H
NMR, shown in Fig. 3C & D for the 4-heptyl generation 2
dendron. Two distinct doublets at approximately d ¼ 1.12 and
1.18ppm were readily integrated and assigned to the dendron
focal point (Ha) and the reacted generation 1 dendron methyls
(Hb), adjacent to the urethane groups, respectively. Interestingly,
the N–H protons of the six urethane groups of the generation 2
1
dendrons were also readily seen within the H NMR spectra,
Fig. 3E, with distinctly different chemical shifts, suggesting
different environments. Although the chemical shift of the N–H
protons of the two urethane groups near to the focal point (NHd)
did not vary with different surface functionality (d ¼ 6.88ppm),
the resonance of the internal urethanes (NHg) showed a signifi-
cant shift from d ¼ 6.67ppm (4-heptyl surface) to d ¼ 6.61ppm
(cyclohexyl surface) and d ¼ 6.43ppm (t-butyl surface). This
suggests a hydrogen bonding contribution that decreases with
the increasing steric bulk of the surface groups. The t-butyl
surface may prevent interaction between urethanes at the
periphery of the dendrons however the less bulky cyclohexyl, or
flexible 4-heptyl, groups appear to allow a close proximity of the
urethane groups and subsequent hydrogen bonding.
Analysis of the generation 1 dendrimers, coupled to a TAEA
core, by 1H NMR showed an identical chemical shift relationship
for the nine urethane N–H protons. The three core urethanes
exhibited a single resonance at approximately d ¼ 6.78ppm for
all surface groups however the six peripheral urethane N–H
resonances varied from d ¼ 6.66ppm (4-heptyl surface) to d ¼
6.60ppm (cyclohexyl surface) and d ¼ 6.43ppm (t-butyl surface).
Fig. 1 Schematic representation of generation 1–3 dendron formation.
Surface group variation is represented by the coloured wedges (yellow ¼
cyclohexyl, blue ¼ t-butyl and green ¼ 4-heptyl). (A) Generation 1
cyclohexyl functional polyurethane dendron, (B) generation 2 t-butyl
functional polyurethane dendron, (C) gGeneration 3 4-heptyl functional
dendron, (D) generation 4 cyclohexyl functional polyurethane dendron.
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Fig. 4 Solution phase IR spectra of polyurethane dendrimers; (A) t-
butyl functional generation 1 dendrimer with deconvolution, (B) gener-
ation 1–3 4-heptyl functional dendrimers.
Fig. 3 Indicative 1H and 13C nuclear magnetic resonance spectra for 4-
heptyl functional materials; (A) generation 1 dendron, (B) 1H NMR
spectrum of the generation 1 dendron (CDCl3), (C) generation 2 dendron,
generation 3 ¼ 80%) however the t-butyl functional dendrimers
did show a systematic increase (generation 1 ¼ 73%, generation
2 ¼ 75%, generation 3 ¼ 80%). If 80% involvement of the
urethane N–H groups is considered to be a limiting maximum for
these structures (based on the 4-heptyl functional dendrimers) it
appears that the t-butyl groups prevent the urethanes in the
peripheral regions of the dendrimers from achieving a proximity
that allows the formation of hydrogen bonds at low generation
however as dendrimer generation increases, the internal urethane
layers are able to hydrogen bond and potentially some peripheral
hydrogen bonding is also possible.
Analysis of the 13C NMR spectra again showed complexity
derived from the chiral nature of the secondary carbon generated
from the ring opening of propylene oxide. When the alcohol is
reacted to form a urethane, the carbon resonance was seen at
approximately d ¼ 71ppm as a relatively broad peak. The
unreacted C–OH at the focal point of each dendron however was
seen as split into three separate peaks between d ¼ 66–66.4ppm in
the ratio of approximately 2 : 4 : 1.6 probably due to the ratios of
R and S enantiomers and the proximity of the nitrogen atom
allowing the potential for interaction with the hydroxyl group.
The urethane carbonyl carbon was clearly observed at approxi-
mately d ¼ 157 ppm, Fig. 3F & G, and also displayed splitting
which was assigned to the different environments within the
various regions of the dendrimer generations. Ester carbonyl
peaks at approximately d ¼ 165 ppm were observed when
coupling to BTT. In total twenty-six new dendritic structures
were synthesised as part of this study, Fig. 5, however a number
of possible structures were omitted to allow focus on, and study
of, systematic variations within specific sequences.
(D&E)1H NMR spectrum of the generation 2 dendron (CD3OD), (F) 13
C
NMR spectrum of the generation 3 dendron (CD3OD), (G) 13C NMR
spectrum of the generation 3 dendrimer (CD3OD) coupled with tris(2-
aminoethyl) amine.
Higher generation dendrimers showed considerable overlap and
definitive data was difficult to obtain. For example, the genera-
tion 3 t-butyl functional dendrimer (TAEA core) showed two
N–H resonances at d ¼ 6.71ppm and d ¼ 6.42ppm, however the
signal at d ¼ 6.71ppm was broad and may correspond to several
layers of overlapping signals but the resonance at d ¼ 6.42ppm is
identical to the earlier t-butyl functional dendrimers. This
suggests the outer layers of the dendrimer do not readily
hydrogen bond when this surface group is present however
internal layers are able to do so to some degree.
To explore the hydrogen bonding further, generation 1–3
dendrimers with 4-heptyl and t-butyl surfaces were studied using
solution-phase infrared spectroscopy in CH2Cl2, Fig. 4. The
N–H stretching frequency, at approximately 3450 cmꢀ1, varies
(to lower wavenumber) and broadens when it is involved in
hydrogen bonding.12 Deconvolution of the complicated dual
signal from 3200–3500 cmꢀ1, Fig. 4A, allows an approximation
of the percentage of hydrogen-bonded urethane groups, after
subtraction of the pure solvent spectrum. Each sample was
repeated three times to generate an average percentage of
hydrogen bonding. The 4-heptyl functional dendrimers, Fig. 4B,
showed no meaningful change in hydrogen bonding with
increasing generation (generation 1 ¼ 79%, generation 2 ¼ 80%,
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Glass transition temperature studies
Tg than the corresponding dendrimers. Within the dendron
series, the flexible 4-heptyl aliphatic surface group generated
lower values of Tg than the other more sterically crowded surface
groups; cyclohexyl generally produced the highest values.
Although the series of aromatic and aliphatic core dendrimers is
incomplete, the 4-heptyl surface group yielded the lowest Tg
values for both cores however the t-butyl surface functionality
appears to exhibit higher Tgs than the cyclohexyl functionality
above generation 2 when using TAEA as the core molecule. The
cyclohexyl group generated the highest Tg values for dendrimers
with the rigid aromatic BTT core.
There have been many studies that have investigated the Tg of
dendritic polymers and shown the effect of changing end group
chemistry, core chemistry and generation number.13 Several
studies have concluded that the conventional Flory–Fox equa-
tion, eqn (1), relating Tg to the reciprocal of molecular weight
(1/M), with the intercept correlating to Tg at infinite molecular
weight (TgN), does not fully represent dendrimer behaviour as
the number of end-groups within dendritic polymer structures
(including the focal point of dendrons) are not insignificant at
very high molecular weights.8,9 Other groups have concluded that
the 1/M relationship is pertinent to dendritic polymers.14 Within
this study, we have measured the Tg of the polyurethane den-
drimers, with TAEA and BTT cores, and dendrons to investigate
effects of the systematic change of surface functionality, core
chemistry and generation within this new series of dendritic
polymers. The data is summarised in Table 1 and consistently
shows increasing Tg with generation, as expected. Tg values were
distributed from ꢀ40 ꢁC to 50 ꢁC and dendrons exhibited a lower
Thermal studies of polyurethane dendrimers
As mentioned above, there have been several reports suggesting
that the Flory–Fox equation is not relevant to the prediction of
T
gN for some dendrimers and others that claim direct relevance
for other materials. We have analysed this polyurethane den-
dron/dendrimer series using three approaches; conventional
Flory–Fox, modified Flory–Fox (considering number of chain
Fig. 5 Schematic representation of polyurethane dendrons and dendrimers within this study. (A) Polyurethane dendrons, (B) polyurethane dendrimers
using tris(2-aminoethyl)amine cores and (C) polyurethane dendrimers using 1,3,5-benzene tricarbonyl trichloride cores. KEY: Surface groups -
cyclohexyl (yellow), t-butyl (blue) and 4-heptyl (green); grey molecules were not synthesised.
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Table 1 Experimental and calculated parameters for polyurethane dendrons and dendrimers with varying generation and surface chemistry
1/M
(Daꢀ1 ꢂ 10ꢀ3
(ne/M)-(ne/M)N
(Daꢀ1 ꢂ 10ꢀ3
Sample
Type
Core
M (g molꢀ1
)
ne
)
)
Tg (ꢁC)
A (Da)
B (Da)
C (Da)
G1-cyclohexyl
G2-cyclohexyl
G3-cyclohexyl
G4-cyclohexyl
G1-t-butyl
Dendron
Dendron
Dendron
Dendron
Dendron
Dendron
Dendron
Dendron
—
—
—
—
—
—
—
—
413.56
1040.36
2293.96
4801.16
361.49
936.21
2085.66
445.65
1104.53
2422.31
1464.91
3345.31
1308.68
3032.85
6481.19
1561.17
3537.82
7491.14
1396.78
3277.19
7037.99
1240.56
2964.73
6413.07
1493.04
3469.70
2
4
8
16
2
2.418
0.961
0.436
0.208
2.766
1.068
0.479
2.244
0.905
0.413
0.683
0.299
0.764
0.330
0.154
0.641
0.283
0.168
0.716
0.305
0.142
0.806
0.337
0.156
0.670
0.423
1.645
0.654
0.297
0.142
2.053
0.793
2
30
40
48
ꢀ6
25
40
ꢀ40
-4
11
39
44
38
47
49
7
17
19
40
48
50
35
47
49
-2
213.24
213.24
213.24
213.24
213.24
213.24
213.24
213.24
213.24
213.24
415.49
415.49
415.49
415.49
415.49
415.49
415.49
415.49
483.61
483.61
483.61
483.61
483.61
483.61
483.61
483.61
200.32
200.32
200.32
200.32
148.25
148.25
148.25
232.41
232.41
232.41
1049.42
1049.42
893.19
893.19
893.19
1145.69
1145.69
1145.69
913.17
913.17
913.17
756.95
756.95
756.95
1009.42
1009.42
313.40
313.40
313.40
313.40
287.37
287.37
287.37
329.45
329.45
329.45
940.20
940.20
862.09
862.09
862.09
988.34
988.34
988.34
940.20
940.20
940.20
862.09
862.09
862.09
988.32
988.32
G2-t-butyl
G3-t-butyl
4
8
0.356
1.452(2.905)a
0.586(1.172)a
G1-4-heptyl
G2-4-heptyl
G3-4-heptyl
G1-cyclohexyl
G2-cyclohexyl
G1-t-butyl
2(4)a
4(8)a
8(16)a
6
Dendron
Dendron
—
—
0.267(0.5344)a
0.905
0.396
Dendrimer
Dendrimer
Dendrimer
Dendrimer
Dendrimer
Dendrimer
Dendrimer
Dendrimer
Dendrimer
Dendrimer
Dendrimer
Dendrimer
Dendrimer
Dendrimer
Dendrimer
Dendrimer
TAEA
TAEA
TAEA
TAEA
TAEA
TAEA
TAEA
TAEA
BTT
BTT
BTT
BTT
BTT
BTT
BTT
BTT
12
6
12
1.105
0.477
0.223
G2-t-butyl
G3-t-butyl
24
G1-4-heptyl
G2-4-heptyl
G3-4-heptyl
G1-cyclohexyl
G2-cyclohexyl
G3-cyclohexyl
G1-t-butyl
G2-t-butyl
G3-t-butyl
G1-4-heptyl
G2-4-heptyl
6(12)a
12(24)a
24(48)a
6
0.808(1.616)a
0.356(0.713)a
0.168(0.337)a
1.105
12
24
6
12
24
6(12)a
12(24)a
0.471
0.219
1.357
0.568
0.262
0.983(1.966)a
0.423(0.846)a
—
a
Figures in brackets are derived from consideration of the 4-heptyl surface group as 2 chain ends.
ends) and a new approach that relates Tg to mathematical
constants that define the geometric relationship of molecular
weight increase and generation number, thereby essentially
reducing the end group number to a mass relationship.
density, N is Avogadro’s number, q is the free volume per chain
end, a is the free volume expansion coefficient, ne is the number
of end groups and M is the molecular weight of the dendritic
polymer.
ꢀ
ꢁꢀ
ꢁ
rNq
ne
Tg ¼ TgN
ꢀ
(2)
Conventional Flory–Fox analysis of Tg
a
M
The Flory–Fox equation is shown in eqn (1) and a plot of Tg vs.
1/M generates a straight line with a slope K (a polymer-depen-
dent constant) and a predicted TgN, determined by the intercept
at the y axis.
As the system specific terms (r, N, q and a) are constant,
a simplified equation, eqn (3) was derived which closely resem-
bles the Flory–Fox equation, eqn (1). This was however modified
further to incorporate a corrective second term, eqn (4), due to
K
Tg ¼ TgN
ꢀ
(1)
M
The conventional Flory–Fox analysis for the ten dendrons
synthesised during this study, Fig. 5A, is shown in Fig. 6. Similar
plots were generated for the dendrimers with TAEA and BTT
cores (ESI†) and the derived TgN values are shown in Table 2;
correlation coefficients ranged from 0.980 to 0.998. The data
suggests that the cyclohexyl functional dendrons are closely
approaching the predicted TgN at generation 4.
The dendrons with the other functional groups are approxi-
mately 10 ꢁC lower than the predicted TgN at generation 3;
dendrimers with either the TAEA or BTT cores appear to be
within 5 ꢁC of their respective TgN values by generation 3.
Modified Flory–Fox analysis of Tg
In a relatively early paper investigating the Tg of dendritic
polymers, Wooley et al.9 suggested that a modification of the
Flory–Fox equation was required and derived eqn (2), where r is
Fig. 6 Flory–Fox analysis of Tg vs. 1/M for polyurethane dendrons.
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Table 2 Determined values of TgN for all study materials
values for (ne/M)N must be derived mathematically from a plot
of ne/M vs. dendrimer generation for each material/surface type
of interest, Fig. 7.
Surface Functionality
Type
Core
T
gN (ꢁC)a
The relationship of ne/M with dendrimer generation is readily
calculated (ESI) as dendritic polymer molecular weight follows
a specific geometric progression dependent on the nature and
multiplicity of branching and the molecular weight of the
constituent repeating and core units. For example, the molecular
weight, M, of the cyclohexyl functional dendrons follows
a simple progression with respect to generation, G, defined by
MGn ¼ 2(MGnꢀ1) + A and, due to the AB2 nature of the
branching group, ne increases as 2Gn. The value A is a constant
correction factor which relates to the core chemistry (also
considering the focal repeat unit of a dendron as a core), and
molecular weight but is consistent within each material series,
Table 1. For example, all dendrons, irrespective of surface
functionality have A ¼ 213.24 Da; values of 415.49 Da and
483.61 Da were determined for the TAEA and BTT core den-
drimers respectively.
cyclohexyl
t-butyl
4-heptyl
cyclohexyl
t-butyl
4-heptyl
cyclohexyl
t-Butyl
Dendron
Dendron
Dendron
Dendrimer
Dendrimer
Dendrimer
Dendrimer
Dendrimer
Dendrimer
—
—
—
TAEA
TAEA
TAEA
BTT
BTT
BTT
50.114
48.875
21.071
47.795
52.301
23.450
52.457
53.029
—
4-heptyl
a
TgN values are shown to 3 decimal places to emphasise similarity of
techniques.
the finite, and constant, value of ne/M at infinite molecular
weight in dendritic polymers, Fig. 7.
ꢀ
ꢁ
ne
Tg ¼ TgN ꢀ K0
(3)
(4)
M
Extrapolation of molecular weight and number of surface
groups to very high generation, using this approach, shows
a constant value of (ne/M) after generation 16–18, and (ne/M)N is
determined as 3.1908 ꢂ 10ꢀ3 Daꢀ1 for the cyclohexyl functional
materials (ESI). This value of (ne/M)N is consistent across the
dendrons, TAEA and BTT core dendrimers with the cyclohexyl
functionality and therefore relates predominantly to the dendron
composition. The value changes with respect to the different
surface functionalities and (ne/M)N values of 3.4799 ꢂ 10ꢀ3 Daꢀ1
and 3.0354 ꢂ 10ꢀ3 Daꢀ1 (ESI†) were determined for the materials
with the t-butyl and 4-heptyl surface functionalities, Fig. 7.
When using this approach, a specific issue arises for func-
tionalities such as the 4-heptyl surface group. When considering
the group as a single chain end, the (ne/M)N value is readily
determined however it is also plausible to consider this func-
tionality as possessing two alkyl end groups per 4-heptyl chain
and therefore ne increases as 2G+1 and a value of 6.0708 ꢂ 10ꢀ3
Daꢀ1 is determined for (ne/M)N, Fig. 7Ci. This value is exactly
double the value determined by considering the 4-heptyl group as
a single chain end and is potentially important in the determi-
nation of TgN using eqn (4).
ꢀ
ꢁ
ꢂ
ꢃ
ne
ne
Tg ¼ TgN ꢀ K0
ꢀ
M
M
N
As for the Flory–Fox equation, a plot of experimental Tg vs.
[ne/M ꢀ (ne/M)N] will produce a prediction of TgN at the y-axis
intercept of the straight line however to exploit this approach, the
The plots of Tg vs. [ne/M ꢀ (ne/M)N] for each series of mate-
rials were constructed as described for the conventional Flory–
Fox approach and TgN values were determined. Surprisingly,
and contradictory to many earlier reports, the values of TgN were
identical (to at least three decimal places) to those determined via
the conventional Flory–Fox equation and shown in Table 1.
Also, the treatment of the 4-heptyl group as a single or double
end group made no difference to the calculated TgN but simply
modified the slope of the straight line plot. The analysis for the
ten dendrons is shown in Fig. 8, with additional plots for the 4-
heptyl functional dendron plotted as (a) considering the 4-heptyl
group as 2 chain ends, and (b) using the conventional Flory–Fox
analysis.
As can be readily observed, the three plots for the 4-heptyl
functional materials converge on exactly the same value for TgN
and this is seen for all materials, dendron or dendrimer, within
this study (ESI†). No negative influence of the focal point
functionality was seen, as reported by, and corrected for, in
previous studies.
Fig. 7 Determination of (ne/M)N for polyurethane dendrons and den-
drimers with (A) cyclohexyl surface functionality, (B) t-butyl surface
functionality and (C) heptyl surface functionality considered as either (i)
a single chain end or (ii) as two chain ends.
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It is surprising that the original Wooley et al.9 report intro-
ducing eqn (2)–(4), did not demonstrate and compare the
conventional Flory–Fox analysis of the twenty-two dendritic
materials studied, however we have reanalysed the data within
the early report and find that both approaches determine an
identical value of TgN (ESI†) with the plots differing only in
slope.
Scaling of dendritic polymer molecular weight based on
AB2 branching can be described purely in terms of the
constants A and B, eqn (7), and further simplified to yield
eqn (8).
MGn ¼ B2Gnꢀ1 + (A[(2x2Gnꢀ1) ꢀ 1])
MGn ¼ B2Gnꢀ1 + A2Gn ꢀ A
(7)
(8)
The number of end groups, ne, also scales as a geometric
progression which is determined by the multiplicity of the
core, D, branching group (in this case 2) and generation,
eqn (9).
Analysis of Tg using geometric parameters
The strong correlation we have observed between the conven-
tional Flory–Fox analysis and the end group-modified Flory–
Fox analysis suggests a relationship between both approaches
that has been overlooked in the assumptions that both the
number of end groups and the non-zero value of (ne/M)N play
important roles in TgN determination for dendritic polymers. We
have therefore derived a new approach that examines the
modified Flory–Fox equation solely using the factors derived
from the geometric progression of dendritic polymer molecular
weight and defines end group number purely in terms of factors
relating to molecular weight.
ne,Gn ¼ D2Gn
(9)
The term ne/M can now be described purely in terms of
generation, core multiplicity and the geometric constants A and
B for any given dendritic polymer series, eqn (10), and simplified
to give eqn (11).
ne;Gn
MGn
D2Gn
B2Gnꢀ1 þ A2Gn ꢀ A
¼
(10)
(11)
As stated earlier, the geometric progression of dendrimer
molecular weight can be represented as eqn (5), where A is
a correction factor that relates to the molecular weights of its
components and is readily calculated (ESI†).
ne;Gn
MGn
D
¼
B
A
2Gn
þ A ꢀ
2
A new constant, C, may be defined as B/2 + A to aid further
simplification and the derivation of eqn (12). Values of C are
shown in Table 1 and show a lack of dependence on dendrimer
core type.
MGn ¼ 2(MGnꢀ1) + A
(5)
Considering the case of the generation 1 dendritic polymer,
another constant of the geometric progression, B, can be
determined as described in eqn (6), and is purely the molec-
ular weight of the generation 1 polymer minus the correction
factor. Values of B for the polyurethane materials within our
study are included in Table 1. Unlike the constant A, B
varies with both surface functionality and dendrimer core
chemistry.
ne;Gn
MGn
D
¼
(12)
A
C ꢀ
2Gn
As a dendritic polymer approaches infinite molecular weight,
the term A/2Gn approaches zero therefore the term (ne/M)N
approaches a constant value calculated as D/C. It is now readily
seen that the term [ne/M ꢀ (ne/M)N] can be represented purely in
terms of A, C and D, eqn (13), which yields eqn (14) and
subsequently eqn (16) via eqn (15).
B ¼ MG1 ꢀ A
(6)
ꢂ
ꢃ
ne;Gn
MGn
ne
D
D
C
ꢀ
¼
ꢀ
(13)
A
M
N
C ꢀ
2Gn
ꢀ
ꢁ
A
CD ꢀ D C ꢀ
ꢂ
ꢃ
2Gn
ne;Gn
ne
ꢀ
ꢁ
ꢀ
¼
(14)
A
MGn
M
N
C C ꢀ
2Gn
A
D
ꢂ
ꢃ
ꢃ
ne;Gn
MGn
ne
2Gn
ꢀ
¼
(15)
(16)
A
M
N
C2 ꢀ C
2Gn
ꢂ
ne;Gn
MGn
ne
DA
GnC2 ꢀ CA
ꢀ
¼
2
M
N
Eqn (16) may be incorporated into eqn (4) to yield eqn (17). As
Fig. 8 Comparison of TgN using conventional and modified Flory–Fox
analysis.
the term D and A are constants, derived from the specific
1106 | Soft Matter, 2012, 8, 1096–1108
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dendritic polymer, these terms may be incorporated into the
constant K0, yielding a new constant K00 and the simplified eqn
(18). This suggests that a plot of Tg,Gn vs. 1/(2GnC2 ꢀ CA) will
generate a straight line with a slope K00 and a y-axis intercept
of TgN
.
ꢀ
ꢀ
ꢁ
ꢁ
DA
GnC2 ꢀ CA
Tg;Gn ¼ TgN ꢀ K0
Tg;Gn ¼ TgN ꢀ K00
(17)
(18)
2
1
2
GnC2 ꢀ CA
The implications of eqn (18) are that TgN may be determined
purely using the constants C and A, and the dendritic
polymer generation, G. Both C and A are mass terms and
plots derived from eqn (18) do not require consideration of
whether the material is a dendrimer or dendron, core multi-
plicity, end group type or number of end groups. Eqn (18) is
therefore a modification of the Flory–Fox equation only in
defining the mass term M through geometric parameters of the
evolution of molecular weight with generation. The assump-
tions that the unusual number of end groups, lack of entan-
glement or globular nature of dendritic polymers require
specific inclusion within any analysis of Tg appear to be
unfounded.
The term 1/(2GnC2 ꢀ CA) has units of Daꢀ2 and is therefore
highly related to the Flory–Fox equation and the modified
Flory–Fox equation (eqn (4)). As such, it is expected that the
value of TgN derived from all three analyses will be identical but
the plots will exhibit different slopes as the constants K, K0 and
K00 contain different terms.
Fig. 9 Comparison of TgN determination using geometric parameters,
conventional and modified Flory–Fox analyses.
We have plotted all twenty six polyurethane study materials
on a single Tg vs. logM graph, Fig. 10. Interestingly, the
dendrimers and dendrons within a surface functionality series,
and irrespective of core chemistry, appear to follow a single
trend. Additionally, the cyclohexyl functional and the t-butyl
functional dendritic materials follow a very similar trend
within the molecular weight range studied here. This is
consistent with the trends for derived TgN values shown in
Table 2. The 4-heptyl functional materials showed consider-
ably different observed Tg values at all molecular weights and
across all material types, again consistent with the results
in Table 2.
Eqn (18) was utilised to generate the analogous Tg vs. 1/(2GnC2
ꢀ CA) plots for all of the polyurethane materials generated
during this study. Two examples of the analyses, cyclohexyl
functional dendrimers (BTT core) and 4-heptyl functional den-
drimers (TAEA core) are shown in Fig. 9 and a comparison of
the Flory–Fox and modified Flory–Fox analyses is included for
one of the examples.
As can be seen, although the slopes are different, the three
analyses lead to identical values (at least three decimal places) for
TgN (ESI†). When applied to the polyurethane materials
described here, all analyses gave TgN values as shown in Table 2.
Finally, re-analysis of the original data within the
Wooley et al.9 report using the geometric progression
approach described above (eqn (18); A ¼ 104 Da, B ¼ 216 Da,
C ¼ 212 Da) generated identical results to the Flory–Fox
and modified Flory–Fox equation within 2 decimal figures
(ESI†).
Relationship of Tg with molecular weight
The relationship of Tg vs. logM is often plotted for linear and
dendritic polymers and has been shown to plateau at relatively
low generations (generation 3 onwards).15 The plateau region is
rationalised within linear polymer samples as the onset of
significant entanglement and therefore the attainment of
a consistent Tg. Within dendritic polymers, the expanded-to-
globular transition is considered as the most appropriate ratio-
nale for the plateau region.
Fig. 10 Variation of Tg with log M for all polyurethane dendrons
and denrimers synthesised during the study (stars
circles ¼ TAEA core dendrimers, squares ¼ BTT core dendrimers;
red cyclohexyl, green t-butyl, blue 4-heptyl surface
functionalities).
¼
dendrons,
¼
¼
¼
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2 M. Calderon, M. A. Quadir, M. Strumia and R. Haag, Biochimie,
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ꢁ
3 J. M. J. Frechet, J. Polym. Sci., Part A: Polym. Chem., 2003, 41,
Conclusions
The selective chemistry of CDI and CDI derivatives has been
shown to be effective in the controlled convergent synthesis of
a range of new polyurethane dendrons, to generation 4, and
dendrimers, to generation 3. Variation of surface functionality
and core chemistry has been successfully achieved and highly
pure materials have been isolated. The library of twenty-six new
materials provided an opportunity to study the effects of den-
drimer structure on Tg and during our evaluation, we have seen
that the conventional Flory–Fox equation accurately determines
TgN without the widely accepted modifications for ‘dendrimer-
relevant’ considerations such as the large number of end groups.
It appears that early reports claiming the need for the modified
approach did not fully compare the Tg vs. 1/M relationship for
the aromatic ether dendrimer materials studied. Our re-analysis
of the early data has shown no significant difference to the
conventional Flory–Fox analysis.
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During the evaluation, it became clear that the factors M and
ne may be represented purely in terms of the generation depen-
dent geometric progression of molecular weight. A new approach
to dendrimer TgN determination has therefore been developed
which generates identical values to the Flory–Fox equation and
is independent of dendrimer chemistry, core/end group multi-
plicity or bias from the analysis of dendrons or dendrimers.
Indeed, the derivation of this approach directly from the previ-
ously reported modified Flory–Fox equation, and the reduction
of this modified equation solely to mass-related terms, demon-
strates the actual relationship of all approaches studied here to
dendrimer molecular weight. Each approach simply provides
a different multiplier that modifies the slope of the Tg vs.
molecular weight relationship but has no influence on the inter-
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.
Within the study of Tg, the effect of surface functionality
changes were most evident for the flexible 4-heptyl surface group,
showing significantly lower Tg than comparable materials with
different surface groups. The presence of cyclohexyl and t-butyl
groups yielded very similar values of Tg across all dendrons and
dendrimers studied, that lie on a similar Tg vs. log M curve.
Future studies will aim to establish the validity of the use of
geometric parameters in the evaluation of TgN across a wide
range of dendrimer chemistries and investigate the need for
variation from the conventional Flory–Fox approach to TgN
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Acknowledgements
The authors wish to thank the Engineering and Physical Sciences
Research Council (EPSRC) and Unilever for funding. Rob
Rannard is also warmly thanked for help compiling the manu-
script. Considerable thanks are also extended to Prof. Norman
Billingham (University of Sussex) for proof-reading and discus-
sion regarding the implications of the geometric progression
approach presented.
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