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Synthesis and self-assembly of amphiphilic star/linear-dendritic polymers: effect of core-vs-peripheral branching on reverse micelle aggregation Karolina Anna Kosakowska, Brittany Kaylee Casey, Julie N. L. Albert, Yang Wang, Henry S Ashbaugh, and Scott Michael Grayson Biomacromolecules, Just Accepted Manuscript • DOI: 10.1021/acs.biomac.8b00679 • Publication Date (Web): 09 Jul 2018 Downloaded from http://pubs.acs.org on July 10, 2018

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Biomacromolecules

Synthesis and self-assembly of amphiphilic star/linear-dendritic polymers: effect of core-vsperipheral branching on reverse micelle aggregation Karolina A. Kosakowska

†,§

, Brittany K. Casey †, Julie N. L. Albert ‡, Yang Wang ‡, Henry S.

Ashbaugh‡, Scott M. Grayson †, * †

Department of Chemistry, Tulane School of Science and Engineering, Tulane University, New Orleans LA 70118 ‡

Department of Chemical and Biomolecular Engineering, Tulane School of Science and Engineering, Tulane University, New Orleans LA 70118

§

Bioinnovation PhD Program, School of Science and Engineering, Tulane University, New Orleans LA 70118 *Correspondence to S.M. Grayson (e-mail: [email protected])

KEYWORDS. Polymer architecture, branching location, reverse micelle, amphiphilic selfassembly, nanoparticle analysis, computational chemistry, transdermal drug delivery

ACS Paragon Plus Environment

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ABSTRACT. A series of branched polymers, consisting of a poly(ethylene glycol) (PEG) core and lipophilic peripheral dendrons, were synthesized and their self-assembly into reverse micelles studied towards the ultimate goal of carrier-mediated transdermal drug delivery. More specifically, this investigation systematically explored the structure-property contributions arising from location and extent of branching by varying the number of branch points at the core and the generation of dendrons at the polar/non-polar interface. For branching at the core, PEGs were selected with one, two or four arms, with one terminal functionality per arm.

For

peripheral branching, end groups were modified with polyester dendrons (of dendritic generations 0, 1 and 2) for each of the three cores. Finally, lauric acid (LA) was used to esterify the periphery, yielding a library of branched, amphiphilic polymers.

Characterization of these

materials via MALDI-TOF MS, GPC and NMR confirmed their exceptionally well-defined structure. Furthermore, atomic force microscopy (AFM) and dynamic light scattering (DLS) confirmed these polymers’ abilities to make discrete aggregates.

As expected, increased

multiplicity of branching resulted in more compact aggregates; however, the location of branching (core versus periphery) did not seem as important in defining aggregate size as the extent of branching. Finally, computational modeling of the branched amphiphile series was explored to elucidate the macromolecular interactions governing self-assembly in these systems.

INTRODUCTION It is estimated that one quarter of the patient population fails to adhere to their physician’s recommended treatment regimens1, resulting in a substantial toll on human health and global healthcare economics.2 Transdermal drug delivery offers a non-invasive route of parenteral drug administration3,4, which can address this problem, particularly for the aging global patient


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population. Appropriately designed transdermal carriers offer the promise of controlled release and tunable multidrug formulations that could result in simplified dosage requirements.5 Over the past few decades, research pertaining to carrier-mediated drug delivery has advanced the field of polymer therapeutics from bench-top proofs-of-concept to effective bed-side applications,6 providing access to more refined temporal drug release for the treatment of diseases.7,8 However, polymeric carriers utilized for transdermal drug delivery must address several unique challenges which require tailored design.9,10 Skin consists a natural barrier to foreign infiltration11-13 in which the outermost layer—the highly lipophilic stratum corneum (SC)—presents the greatest impediment to permeation.14,15 Thus, successful transdermal carriers must efficiently load drug, enable transport across the SC and maintain therapeutic payload delivery into the underlying tissue. Addressing these restrictions, carriers designed for transdermal drug delivery must be small and stable enough16,17 to traverse the narrow labyrinth-like passages of the SC,18,19 while simultaneously maintaining a high encapsulation capacity to achieve therapeutic levels of systemic drug availability.20,21 Furthermore, the carriers need to be sufficiently biocompatible and biodegradable as to minimize undesirable side effects from the polymer itself.22 Towards this end, dendrimer-based drug delivery systems have recently gained interest for dermal and transdermal drug delivery application23-25. In the present study, self-assembled, reverse micelle carrier consisting of a dendronized lipophilic corona surrounding an internal polar microenvironment are designed to allow for the solubilization and transport of a polar drug in the lipophilic dermis. Once crossing the outer skin, the change in the surrounding tissue polarity going from the hydrophobic SC to the underlying hydrophilic epidermal tissue can trigger the disruption of the aggregates and release of the drug payload.8,26 The multiple design constraints


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required for successful self-assembly, drug encapsulation, transdermal transport, and drug release, as well as concerns for biocompatibility and pharmacokinetics validate a modular approach for synthesizing amphiphilic carriers, where multiple structural parameters can be varied and then tested empirically. Hence, this work studies the effect of branched polymer architecture on dynamic amphiphilic self-assembly behavior, specifically investigating the extent to which the location of branching— core versus peripheral—influences aggregate properties pertinent to carrier-mediated transdermal drug delivery.

It is well known that sophisticated topology (i.e. star, graft, cyclic,

hyperbranched, dendritic, etc.) significantly impacts physical material properties such as solubility,27,28 rheology,29-31 and thermal properties,32,33 to name a few. Likewise, the effects of polymer architecture on amphiphilic behavior have been extensively explored, due in part to the biologically relevant applications of self-assembled materials.34 For example, Meijer et al. observed generation-dependent aggregate morphology in the self-assembly of poly(styrene)dendritic-poly(propylene imine) (PS-d-PPI), which transition from vesicles (PS-[G3]-PPI) to micellar rods (PS-[G4]-PPI) and finally to spherical micelles (PS-[G5]-PPI) upon increased dendritic branching.35,36 Architecture can also be used to afford aggregate equilibrium stability. Whereas multicomponent micelles self-assemble only above a threshold critical micelle concentration (CMC),37,38 highly-branched amphiphilic polymers can exist as “unimolecular micelles” instead.39 As such, unimolecular micelle dendrimers prepared by Hawker et al. retain the ability to encapsulates guests even at very low concentrations.40 Previous work in our group has explored the effect of branching in dendritic-core-star polymers with amphiphilic arms consisting

of

poly(oligo(ethylene

glycol)

methacrylate)-block-poly(lauryl

methacrylate)

(pOEGMA-b-pLMA) copolymers. In this preceding study, it was determined that increasing


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core branching (e.g. from 6 to 12 arms) lowered the CMC and improved the encapsulation capacity of the resultant reverse micelle assemblies.41 Similarly, the core-shell architecture of inverted nanocapsules consisting of lipophile-functionalized hyperbranched polyglycerol (PG) was shown by Frey and co-workers to be crucial for uptake and phase transfer of polar dyes, as no encapsulation was observed with analogous linear PG amphiphiles.42,43 Although numerous well-designed studies have been reported demonstrating the important role of polymer architecture in self-assembly, comparisons are generally limited to linear analogs, rather than comparing the role of different types of branching motifs. Thus, less is understood about the impact of branching location within well-defined polymer architectures, e.g. comparing the structure-property relationships of polymers with differing spatial distribution of equivalent branching multiplicity. The present contribution details the modular synthesis of a library of amphiphiles exhibiting systematic control of branching topology, and explores how the extent and location of branching affects the size and stability of self-assembled reverse micelle aggregates. Polar 1-arm, 2-arm and 4-arm poly(ethylene glycol) (PEG) cores are used to probe branching at the polymer center, whereas branching at the periphery is tuned by grafting of aliphatic polyester dendrons at the PEG chain ends. Finally, laurate ester conjugation to the dendritic chain ends yields a lipophilic periphery, providing amphiphiles with a propensity toward self-assembly in non-polar solvents. Detailed material characterization confirms the ability to strictly control structural purity throughout the synthesis of each amphiphile.

Furthermore, computational modeling of the

solvent interaction for individual macromolecules supports the experimental size and dispersity observations. Additional experimental studies evaluating CMC, encapsulation capacity and in vitro transdermal transport for these systems are detailed in a concurrent report.44 This work


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therefore aims to understand the role of branching placement and multiplicity in tuning the selfassembly of amphiphilic polymers into reverse micelle carriers for transdermal drug delivery. EXPERIMENTAL Materials.

Poly(ethylene glycol) monomethyl ether (C1-(PEG-OH)1; Mn = 5,000 Da),

dihydroxy poly(ethylene glycol) (C2-(PEG-OH)2; Mn = 5,000 Da), palladium (Pd/C, 10 wt. % on carbon), lauric acid, 1-ethyl-3-(3-dimethylaminopropyl)carbodiimide (EDC), and 4dimethylaminopyridine (DMAP) were purchased from Millipore-Sigma (St. Louis, MO) and used without further purification.

All solvents were purchased from Fisher Scientific Inc.

(Hampton, NH). 4-Arm PEG-amine hydrochloride (C4-(PEG-NH2)4/HCl, Mn = 5,000 Da) was purchased from JENKEM Technology USA (Allen, TX) and was treated with base prior to use to isolate the free amine. Briefly, 5.80 g C4-(PEG-NH2)4/HCl was dissolved in 650 mL of a 1 M NaOH solution (aq), stirred at room temperature for 2 h and extracted several (4—6) times with 300 mL of dichloromethane (CH2Cl2). The combined organic layers were washed with 2 times with 500 mL of H2O, dried over Na2SO4 and concentrated in vacuo prior to precipitation into excess cold diethyl ether (DEE) to afford amine terminated 4-arm PEG (C4-(PEG-NH2)4). Benzylidene

protected

2,2-bis(hydroxymethyl)propionic

(Bnz-bisMPA)

anhydride

was

synthesized as previously described;45 relevant starting material characterization data is provided in the Supporting Information for Bnz-bisMPA (Fig. S1) and for the 1-arm, 2-arm and 4-arm PEG cores (Figs. S2—S10).

Synthetic experimental details for the obtained branched

amphiphile library are reported in the Supporting Information, with characterization data provided for all stages of polymer modification (Figs. S11—S73). Polymer Characterization. Gel permeation chromatography (GPC) was performed on a system consisting of a Waters Model 1515 isocratic pump and Waters Model 2487 differential


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refractometer detector (Waters Corp., Milford, MA), equipped with two columns in series (PSS SDV analytical linear M (8 x 300 mm) and PSS SDV analytical 100 Å (8 x 300 mm); Polymer Laboratories Inc., Amherst, MA). All data were collected at 30 °C in tetrahydrofuran (THF) at a flow rate of 1 mL min-1; distributions were quantified from PEG calibration standards (Agilent Technologies, Santa Clara, CA) over a 150 g mol-1—70,000 g mol-1 mass range. Matrix-assisted laser desorption/ionization time-of-flight mass spectra (MALDI-TOF MS) were collected in positive-ion reflector mode using a Bruker AutoFlex III MALDI-TOF MS (Bruker Daltonics, Billerica, MA) under a 20 kV accelerating voltage and delayed ion extraction. The detection range was calibrated using SpheriCal dendritic calibration standards (Polymer Factory, Stockholm, Sweden) for all measurements. Samples were prepared in THF (2 mg mL-1) and mixed with 20 mg mL-1 α-cyano-4-hydroxycinnamic acid (matrix) and 1 mg mL-1 sodium trifluoroacetate (cation, 98%, Aldrich) THF solutions at a ratio of 1:4:1, respectively. 3 µL of the combined analyte-matrix-cation solution was deposited onto the target plate via the dried droplet method. Spectral acquisition was performed under the minimum suitable laser intensity and subsequent data analysis was carried out using FlexAnalysis software (Bruker Daltonics). Nuclear magnetic resonance (NMR) analysis was performed using a Varian 400 MHz NMR instrument (Agilent Technologies, Santa Clara, CA) and processed using MestReNova 11.0.0 (Mestrelab Research SL, Santiago de Compostela, Spain).

For proton NMR (1H NMR)

experiments, samples were prepared in (CD3)2SO (2—3 mg mL-1); carbon NMR (13C NMR) experiments were performed on samples in CDCl3 (15—30 mg mL-1); all spectra were collected at ambient probe temperature. Aggregate Preparation and Characterization.

Reverse micelles were prepared by

suspending a predetermined amount of amphiphile in toluene and mixing (via vortex mixer) until


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the solution appeared well-dissolved, typically allowing for the mixture to equilibrate overnight. Varying concentrations of polymer-toluene solutions were prepared via dilution from stock and passed through a 0.2 µm syringe filter (Whatman, Maidstone, UK) prior to analysis. Atomic force microscopy (AFM) measurements were performed using a Bruker Dimension ICON atomic force microscope (Bruker Corp. Billerica, MA) fitted with a Tap150-G probe (Budget Sensors, Sofia, Bulgaria; spring constant 5 N m-1, resonance frequency 150 kHz, length 125 µm). Reverse micelle aggregates were imaged on a hydrophobic substrate comprising silicon wafers (P, NOVA Electronic Materials, Flower Mound, TX) functionalized with a n-butyldimethylchlorosilane (Gelest Inc., Morrisville, PA) monolayer. Silicon wafers were rinsed with toluene and placed in a UVO cleaner (Model 42, Jelight Co., Inc., Irvine, CA) for at least 15 minutes, then re-rinsed with toluene and dried using N2 gas. Modifying reagent was applied directly to the silicon surface (2 h), after which the functionalized substrate was washed repeatedly with toluene and dried prior to use. Dilute polymer solutions (0.01—0.10 mg mL-1) prepared in toluene were drop cast onto a clean modified substrate and gently evaporated using N2 gas. Images were collected in tapping mode recording a minimum of three independent regions per deposited sample. Particle analysis and image preparation was carried out using NanoScope Analysis software (Bruker Corp.)

Dynamic light scattering (DLS) data was

collected using a Brookhaven NanoBrook Omni Particle Sizer (Brookhaven Instruments Corporation, Holtsville NY) and analyzed with Particle Solutions software (version 3.5, Brookhaven). For each species, toluene-suspended amphiphile solutions were prepared at a minimum of two different concentrations (8— 20 mg mL-1, depending on observed count rate), filtered (0.2 µm syringe filter, Whatman, Maidstone, UK) and transferred to clean, toluene-rinsed glass cuvettes, allowing for ~30 min equilibration prior to analysis. All measurements were


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performed in replicate (n ≥ 5) at room temperature using a 90-degree scattering angle (λ = 640 nm), with appropriate dust filter cut-off applied. Particle refractive index was approximated from amphiphile refractive index increment data, obtained in toluene using a Water 410 Refractometer (Waters Corp.) and averaged between various species. Computational Modeling. Molecular simulations for all branched amphiphiles in toluene were performed using GROMACS 5.1.346 in the isothermal-isobaric ensemble. The temperature and pressure were set to set to 25°C and 1 bar and controlled using the velocity rescaling47 and Parniello-Rahman48 algorithms, respectively. The polymer and toluene were modeled using the MARTINI force-field49 with potential interactions detailed in the Supporting Information (Computational Modeling Supplement). Simulations were performed for a single amphiphile (i.e. unimer) in solution for each of the three core PEG (5,000 Da) topologies (1-arm (C1), 2-arm (C2), and 4-arm (C4)) and dendritic generations of peripheral branching ([G0] to [G2]), totaling 9 distinct polymer architectures. Production simulations were conducted for 50 ns following at least 5 ns for equilibration. Equilibrium averages were determined over 25,000 configurations collected at regular intervals from each simulation. The average solvent accessible surface areas (SASAs) for the PEG, alkyl, and dendritic units were evaluated using the GROMACS program ‘gmx sasa’,50 which uses the double cubic lattice method for area determination. From these surface areas, the percent solvent exposures of PEG and alkyl units for each branched species was calculated relative to total amphiphile SASA.


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RESULTS AND DISCUSSION Synthesis of Branched Amphiphile Library: Tailored Incorporation of Branching at the Core or Periphery of Amphiphilic Polymers. For applications in the transdermal delivery of therapeutics, numerous parameters of the micellar assemblies are of critical importance, including size, shape, and loading capacity of the aggregates.51 In order to understand the role of branching in the self-assembly of amphiphilic materials, a series of laurylated, branched PEG polymers was prepared with control over the location and multiplicity of the branching points. To provide an accurate correlation between these structural parameters and the polymer aggregates’ properties, it is paramount to obtain structurally pure, well-defined polymers. The modular synthetic approach depicted in Scheme 1 proved an efficient means for obtaining exceptionally well-defined amphiphilic macromolecules with an exact number of branching points at the polymer core and/or periphery. To control the extent of core branching, three distinct, commercially available PEG species (Scheme 1) were employed: “1-arm” monohydroxy monomethyl ether PEG (C1-(PEG-OH)1), “2-arm” bisfunctional dihydroxy PEG (C2-(PEG-OH)2) and 4-arm tetrafunctional pentaerythritol-centered PEG-tetraamine (C4-(PEGNH2)4). As chain length is an architectural feature which effects polymers’ physical52–as well as biophysical53—behavior, the molecular weight of each PEG species was kept constant for each core (Mn = ~5,000 Da) to enable direct comparison across the library of branched amphiphiles. Notably, the amine functionality of the C4-PEG core differs from the hydroxyl end groups of 1and 2-arm analogs—due to commercial accessibility of starting materials—however, this replacement of an ester linkage with an amide linkage is expected to have only a minimal effect on the investigated self-assembly properties.


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Scheme 1. General synthesis of branched amphiphile library; modular approach uses divergent dendronization of core molecule functionalities (1-, 2-, and 4-arm PEG) to create linear- and stardendritic hybrids, followed by ester coupling of lipophilic lauric acid moieties to yield amphiphilic materials.


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Table 1. Molecular weight and dispersity characteristics of branched amphiphiles and dendronized intermediates, as obtained from GPC, MALDI-TOF MS and 1H NMR characterization. MALDI

1

GPC

H NMR

Mn,Obs

Mn,Theoa

Ɖ

Mnb

Ɖ

Mn,Calc

Mn,Theoc

C1-(PEG-OH)1

5055

5055

1.006

5020

1.027

5165

5165

C1-(PEG-LE)1

5240

5235

1.005

5330

1.028

5415

5345

C1-(PEG-[G1]-Ph)1

5240

5260

1.003

5340

1.028

5360

5370

C1-(PEG-[G1]-OH2)1

5180

5170

1.002

5260

1.030

5300

5280

C1-(PEG-[G1]-LE2)1

5545

5535

1.003

5610

1.030

5625

5645

C1-(PEG-[G2]-Ph2)1

5560

5580

1.005

5580

1.027

5765

5690

C1-(PEG-[G2]-OH4)1

5390

5405

1.004

5320

1.023

5560

5515

C1-(PEG-[G2]-LE4)1

6130

6135

1.003

6280

1.027

6200

6245

C2-(PEG-OH)2

4800

4800

1.006

4640

1.031

4990

4990

C2-(PEG-LE)2

5175

5165

1.003

5270

1.030

5320

5355

C2-(PEG-[G1]-Ph)2

5160

5210

1.003

5110

1.030

5380

5400

C2-(PEG-[G1]-OH2)2

5010

5030

1.003

4920

1.030

5255

5220

C2-(PEG-[G1]-LE2)2

5760

5760

1.004

5820

1.030

5980

5950

C2-(PEG-[G2]-Ph2)2

5840

5850

1.004

5510

1.030

5965

6040

C2-(PEG-[G2]-OH4)2

5510

5500

1.004

5230

1.030

5755

5685

C2-(PEG-[G2]-LE4)2

6960

6955

1.002

6850

1.029

7140

7145

C4-(PEG-NH2)4

5225

5225

1.003

4530

1.025

5350

5350

C4-(PEG-LE)4

5985

5955

1.003

5440

1.028

6130

6080

C4-(PEG-[G1]-Ph)4

6030

6040

1.002

4780

1.025

6185

6165

C4-(PEG-[G1]-OH2)4

5710

5690

1.002

4000

1.027

5875

5815

C4-(PEG-[G1]-LE2)4

7140

7150

1.001

6500

1.031

7275

7275

C4-(PEG-[G2]-Ph2)4

7295

7325

1.002

5690

1.031

7535

7450

C4-(PEG-[G2]-OH4)4

6630

6620

1.001

4800

1.029

6835

6745

C4-(PEG-[G2]-LE4)4

9510

9535

1.001

8560

1.033

9750

9660

a

φLE,Calcd φLE,Theoe 3.1

3.1

6.0

5.9

10.9

10.7

6.4

6.2

11.2

11.2

18.7

18.7

10.9

11.0

18.4

18.4

27.7

27.7

b

calculated from respective MALDI-TOF MS Mn values obtained for each PEG core; GPC distributions quantified using PEG standard calibration; c calculated from respective 1H NMR MCalc values obtained for each PEG core; d mass % non-polar groups per total amphiphile mass, calculated from 1H NMR integrations; e mass % non-polar groups per total amphiphile mass, calculated from amphiphile 1H NMR MTheo values.


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For each of the PEG cores, the addition of peripheral branching was achieved through divergent dendronization using 2,2-bis(hydroxymethyl)propionic acid (bisMPA) as the dendritic monomer to prepare biocompatible, biodegradable54 polyester dendrons. Successive coupling with benzylidene-protected bisMPA (Bnz-bisMPA) anhydride and removal of the benzylidene group allowed the iterative synthesis of structurally pure, chain-end dendronized PEGs, with each additional generation ([G#]) doubling the total number of peripheral functional groups.45 This route proved highly efficient, with rapid, quantitative end group conversion and no chromatographic purification required to afford exceptionally well-defined materials in high yield. Finally, to afford amphiphilic character, the requisite non-polar domain was incorporated via active ester coupling of lauric acid to the peripheral functionalities of each star/lineardendritic PEG hybrid architecture; chemical structures of the resultant branched amphiphile library are depicted in Scheme 2. This short chain fatty ester was selected because of its comparable length to the skin lipids in the SC.55 Furthermore, the use of a lipophilic moiety with lower molecular weight (Mw = 200 Da) helped achieve a more balanced polar/non-polar ratio, considering as many as 16 lauryl esters (in the case of C4-(PEG-[G2]-OH4)4, Scheme 2) are attached to each dendronized PEG core. As the relative mass fraction of non-polar groups (mass % non-polar groups per total amphiphile molecular weight, φLE) is expected to play an important role in the self-assembly of the amphiphiles, these values are provided in Table 1. Furthermore, use of a non-polymeric lipophile enables precise determination of structural purity, particularly by MALDI-TOF MS characterization.

For classical block copolymer-based amphiphiles,

complex molecular weight distributions and peak broadening can make it difficult to confirm the quantitative attachment (by techniques such as MS or NMR) of a second block to the homopolymer precursor.56 On the other hand, the laurylated amphiphile MALDI-TOF mass


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spectra exhibit narrow distributions and signals can be easily resolved to confirm comprehensive functional group transformation.57

Scheme 2. Systematic library of branched amphiphile linear- and star-dendritic polymer hybrids, with core and peripheral branching varying along the vertical and horizontal axes, respectively.

To illustrate the ability of mass spectrometry to confirm the exact structure of the proposed amphiphiles, Figure 1 depicts the MALDI-TOF mass spectra of all branched structures derived by functionalization of the C2-(PEG-OH)2 core. Analogous MS figures depicting C1-(PEGOH)1 and C4-(PEG-NH2)4 core modifications are included in Supporting Information (Figs. S74—S75). Through each subsequent synthetic step, obtained mass spectra exhibit the same narrow polymer dispersity as the starting material (Fig. 1, left), although this distribution shifts (higher or lower) relative to the change in end-group mass.

The MALDI-TOF MS Mn values


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after each end-group modification were all within 1% of the theoretical values (Table 1). Furthermore, quantitative end-group conversion can be confirmed by monitoring the exact mass signal shifts of a single oligomer within the polymer distribution. As seen in Figure 1, the C2(PEG-OH)2 104-mer shows a mass shifts of ∆[m/z] = +408.5 Da upon [G1] dendronization and ∆[m/z] = -176.4 Da after the benzylidene deprotection, in close agreement with theoretical values (∆Mtheo = +408.2 and -176.1 Da, respectively). A similar accuracy is observed for the second generation ([G2]) dendronization/deprotection shifts of ∆[m/z] = +816.2 and -351.8 (∆Mtheo = +816.3 and -352.1 Da, respectively). Importantly, during each transformation, no additional MS signals were observed that would indicate incomplete coupling or deprotection, confirming the structural fidelity of the dendritic end-groups. The same MS analysis may be applied to confirm conjugation of the lipophilic lauryl moieties; following esterification with lauric acid (Fig. 1, right), the monoisotopic theoretical masses for the 104-mer of C2-(PEG-LE)2 ([MTheo+Na+] = 4984.04 Da), C2-(PEG-[G1]-LE2)2 ([MTheo+Na+] = 5580.48 Da) and C2-(PEG-[G2]-LE4)2 ([MTheo+Na+] = 6773.53 Da) are in excellent agreement with observed values ([m/z]Obs = 4984.49, 5580.04, and 6773.53 Da, respectively). Thus, quantitative end-group transformation and structural fidelity can be confirmed for all stages of branched amphiphile synthesis.


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Figure 1. MALDI-TOF mass spectra of 2-arm PEG derivatives, ionized with Na+ and using αcyano-4-hydroxycinnamic acid as matrix; synthetic functionalization of a single oligomer (n=104) is highlighted through subsequent dendronization/deprotection steps and peripheral laurylation, with corresponding peak shifts in exact agreement with theoretical values. Quantitative end-group transformation is observed throughout each stage of modification.

GPC characterization further supports the structural purity of the branched amphiphile constructs and intermediate dendritic precursors generated from the three PEG cores. Through each stage of synthetic transformation, obtained chromatograms shift relative to the change in end-group mass, as seen in Figure 2 for the C2-(PEG-OH)2-based analogs. Here, retention time decreases following chain-end dendronization and then increases upon subsequent hydrolytic deprotection (Fig. 2a and 2b). The same can be observed following peripheral laurylation (Fig. 2c), with progressively lower elution times as the amphiphile generation of the laurylated dendrons increases. Analogous GPC chromatogram overlays for the C1-(PEG-OH)1 and C4(PEG-NH2)4 derivatives can be found in the Supporting Information (Figs. S76—S77). For all


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derived compounds, obtained GPC traces maintain narrow dispersity and exhibit no measurable low- or high-molecular weight byproducts. Furthermore, mass distribution analysis against linear PEG calibration standards provided Mn values in generally close agreement with those obtained by MALDI-TOF MS (Table 1).

However, in determining the molecular weight

distribution of the 4-arm PEG analogues, the calculated Mn values by GPC deviated significantly from those obtained by other characterization techniques. This can be attributed to a reduced radius of gyration imposed by the 4-arm core junction, resulting in a more compact nature for the star-shaped polymers when compared to the linear PEG standards.58,59 The effect of core branching on GPC analysis for the branched polymer hybrids is represented graphically in Figure S78 (Supporting Information), which plots the elution volume versus log molecular weight for each of the 1-, 2- and 4-arm derivatives against the linear PEG standards.


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Figure 2. GPC trace data for 2-arm PEG derivatives; (a) overlay of starting material with [G1] dendronized/deprotected species and (b) overlay of [G1] deprotected analogue (dashed line) with subsequent [G2] dendronized/deprotected species; peak retention time enlarged below to show relative mass shift to end-group character; (c) overlay of starting material trace with [G0], [G1] and [G2] laurylated amphiphiles derived therefrom.

Figure 3. 1H NMR spectra monitoring 2-arm PEG core end-group transformations for subsequent [G1] dendronized analogues; (a) 2-arm PEG starting material, C2-(PEG-OH)2; (b) first generation dendronized product, C2-(PEG-[G1]-Ph)2; (c) deprotected dendronized product, C2-(PEG-[G1]-OH2)2; and (d) laurate ester functionalized product, C2-(PEG-[G1]-LE2)2. All spectra were collected in (CD3)2SO; * indicates PEG backbone sideband.

Finally, the purity of all PEG-dendrimer hybrids and subsequent laurate ester-coupled amphiphiles was assessed via NMR characterization. peripheral functionalization can be monitored by

As seen in Figure 3, the extent of 1

H NMR throughout each synthetic

modification, shown here for the [G1]-dendronized 2-arm PEG core derivatives. Following coupling with Bnz-bisMPA, new signals can be observed corresponding to aromatic and


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benzylic protons (Fig. 3b, g and f, respectively); these signals vanish upon the removal of the benzylidene group via hydrogenolysis, however the bisMPA methyl and –CH2– resonances (e and d/d’, respectively) shift and are retained following both deprotection (Fig. 3c) and peripheral laurylation (Fig. 3d). Furthermore, 1H NMR signal integration values indicate quantitative chain-end transformations as the obtained Mn,Calc and φLE values (Table 1) are in excellent agreement with theoretical values (within 2%) for all species described. Both 1H and 13C NMR analysis verified these samples contain no measurably amount of small molecular weight impurities, which may be overlooked more easily by MALDI-TOF MS or GPC characterization techniques; all NMR spectra can be found in the Supporting Information. In summation, a series of systematically branched amphiphiles was generated using an efficient modular approach. By this route, strict control over core and peripheral branching was demonstrated through MALDI-TOF MS, GPC and NMR characterization, all of which confirm the structural and chemical purity of each amphiphilic branched polymer. Owing to the welldefined nature of this systematic library, a direct comparison of self-assembly properties can be used to evaluate the extent to which branching location (core-branched verses peripheralbranched) can affect physical behavior.


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Reverse Micelle Characterization: Effect of Core and Peripheral Branching on Aggregate Size and Dispersity.

Much like conventional aqueous micellization of block

copolymers, reverse micelles are formed from self-assembly of amphiphilic molecules in nonpolar media.60 In assessing the reverse micelle formation of the branched polymer library, physical characterization experiments were conducted in toluene to enable comparison of the data across many different characterization techniques. Thus, for the system under investigation, aggregates feature a solvatophobic (polar) PEG core shielded by a solvent-compatible (nonpolar) laurate ester corona, with peripheral bisMPA dendrons at the core/shell interface. For each branched amphiphile, reverse micelles were evaluated to determine aggregate size and dispersity (detailed below), with subsequent investigations of critical micelle concentration (CMC), encapsulation efficiency and in vitro transdermal diffusion detailed elsewhere.44 Amphiphile aggregation was probed via DLS and AFM characterization to determine the effect of core and peripheral branching on reverse micelle size and dispersity; results are listed in Table 2 for the library of core and peripherally branched amphiphilic polymers. Both light scattering and AFM data verify that the investigated amphiphiles self-assemble in non-polar solvent, with consistent trends observed by both techniques.

Generally, AFM-measured

aggregate diameters and size dispersity values were lower than those obtained by DLS for the majority of branched amphiphiles investigated. The reduced apparent diameter can be attributed to lack of solvent swelling in the solid-state characterization technique,61 as well as possible trapping of non-equilibrium state aggregates during reverse micelle deposition and drying.62 In the case of the three smallest reverse-micelle-forming species (namely, C2-(PEG-[G2]-LE4)2, C4-(PEG-[G1]-LE2)4 and C4-(PEG-[G2]-LE4)4), the opposite trend was observed (i.e. DAFM > DDLS). Here, the deviation is believed to be caused by the tip-broadening effect, whereby the


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small size ( 600 nm), possibly resulting from aggregates of aggregates or large contaminants. However, measurements consistently showed distributions in an intermediate size range (10-200 nm) and these values were averaged and reported in Table 2


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for each reverse micelle aggregate. Additional DLS data for each polymer in the amphiphile library can be found in the Supporting Information (Figs. S82—S90).

Figure 4. Representative AFM height sensor images (1 µm2) of branched amphiphile solid-state aggregates with corresponding particle diameter distributions below, compiled from multiple images; (a) C1-(PEG-LE)1; (b) C1-(PEG-[G1]-LE2)1; (c) C1-(PEG-[G2]-LE4)1; (d) C2-(PEGLE)2; (e) C2-(PEG-[G1]-LE2)2; (f) C2-(PEG-[G2]-LE4)2; (g) C4-(PEG-LE)4; (h) C4-(PEG[G1]-LE2)4; (i) C4-(PEG-[G2]-LE4)4.


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Figure 5. DLS diameter and dispersity values with standard deviation for branched amphiphile aggregates, plotted by (a) and (b) core branching; (c) and (d) peripheral branching.

Structural incorporation of either type of architectural branching (core or peripheral) yielded more compact, better defined aggregates with a smaller apparent diameter and reduced reverse micelle dispersity. Addressing first the effect of core branching, aggregates of the three different cores that exhibited no peripheral branching motifs (i.e. [G0] analogs) are shown in Figure 5a (light gray line) and 5b (light gray columns); amphiphiles C1-(PEG-LE)1, C2-(PEG-LE)2 and C4-(PEG-LE)4 decrease in diameter from 161 nm to 103 nm to 70 nm, as well as in dispersity from 0.43 to 0.38 to 0.33, respectively, as a result of increased core branching. The same can be observed when comparing the three different cores with [G1] peripheral dendronization (Fig. 5a, dark gray line and 5b, dark gray column) and with [G2] branching (Fig. 5a, black line and 5b, black column). Similarly, with increasing peripheral branching for C2-(PEG-LE)2, C2-(PEG-


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[G1]-LE2)2 and C2-(PEG-[G2]-LE4)2, an analogous decrease in diameter and dispersity is seen, from 103 nm to 73 nm to 28 nm and 0.38 to 0.34 to 0.20, respectively. Comparable trends were observed for the reverse micelle properties as a function of peripheral branching for both the 1arm (Fig. 5c, light gray line and 5d, light gray column) and 4-arm (Fig. 5c, black line and 5d, black column) derivatives. Assessing self-assembly across all branched species, amphiphiles of equivalent total functionality (i.e. the product of core and peripheral branching, which correlates directly to the number of lauryl groups per polymer) are seen to form reverse micelles with comparable distribution properties. For example, all three tetra-laurylated amphiphiles (C1-(PEG-[G2]LE4)1, C2-(PEG-[G1]-LE2)2 and C4-(PEG-LE)4) form aggregates with similar observed diameters (64—73 nm) and dispersity (0.32—0.34) values. Notably, similar size ranges are also observed for the bis-laurylated amphiphiles (C1-(PEG-[G1]-LE2)1 and C2-(PEG-LE)2) with diameters of 103—137 nm and dispersity values of 0.38—0.41, as well as for the octa-laurylated amphiphiles (C2-(PEG-[G2]-LE4)2 and C4-(PEG-[G1]-LE2)4) with diameters of 28—33 nm and analogous 0.20 dispersity. Therefore, size and dispersity trends appear to be predominantly driven by the total functionality of the branched amphiphile library, and may also relate to variations in the polymers’ mass fraction of non-polar groups. An increase in branching motifs (regardless of location) corresponds to a greater number of lipophilic laurate ester moieties and, in turn, increases the φLE of corona-forming substituents. Such correlations between aggregation behavior and relative mass fraction of polar and non-polar domains have been broadly investigated in linear block-copolymer self-assembly64-66; yet, because the present library does not probe independently the number of branch points versus this polarity ratio, it is difficult to confirm which effect is more important in defining the aggregation behavior. Nonetheless, the


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observed similarities between structures with core branching and peripheral branching make it clear that the overall number of branches, rather than the location of branching, is the major factor in defining self-assembly in this system. Computational modeling of the solvent accessible surface areas (SASAs) for all investigated branched polymers presents further evidence to support the importance of overall branching, rather than branching location, on the assembly properties of the amphiphile library (Fig. 6). Self-assembly of the amphiphilic unimers is driven by non-covalent solvent-mediated polar/nonpolar interactions, which act to minimize exposure of the solvatophobic PEG chains to the nonpolar media (i.e. toluene). Thus, amphiphiles with a higher unimer %PEG SASA exposure can be expected to form larger reverse micelles to achieve sufficient corona coverage and core shielding.67 As seen in Figure 6a, increasing the amphiphile core branching while holding peripheral dendronization constant reduces %PEG exposure to toluene for each of the three dendron generations, with a concomitant rise in alkyl-solvent contact. Likewise, increasing peripheral branching within a fixed core-branching topology decreases the unimer PEG exposure fraction (Fig. 6b). These trends agree with those observed in Figure 5a and 5c, wherein increasing amphiphile branching at both the core or periphery reduced aggregate size, supporting our expectation that unimer SASA and self-assembly behavior can be correlated. Notably, plotting %PEG and %alkyl group solvent exposure as a function of total alkyl number (i.e. overall branching functionality), the relative extent of unimer shielding appears wholly dependent on the number of branching points/amphiphile mass fraction of solvatophilic alkyl functionalities (Fig. 7). This trend correlates exceptionally well with experimental observations; plotting aggregate size per overall laurate ester functionality alongside SASA in Figure 7 shows a parallel relationship between the amphiphile unimer and self-assembly properties.


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Figure 6. Branched amphiphile SASA toluene exposure fraction of unimer solvatophobic PEG domain (solid line) and solvatophilic alkyl domain (dashed line) plotted by (a) core branching; (b) peripheral branching.

Figure 7. Branched amphiphile SASA toluene exposure fraction (left axis) of unimer solvatophobic PEG (black symbol) and solvatophilic alkyl (gray symbol) domains and corresponding experimentally-obtained reverse micelle diameters (nm, right axis, open red symbol), plotted as a function of total amphiphile alkyl number (1 through 16). Thus, by both computational and experimental studies, the number of alkyl groups (or total branching) in the structures appears to be the most important variable to determining aggregation behavior. Hence, a more detailed comparison of amphiphiles with an identical number of alkyl groups (and therefore equivalent mass fraction of non-polar groups) is depicted in Figure 8, to elucidate some of the subtler effects branching location may have on reverse micelle size trends. First addressing the tetra-laurylated species (Fig. 8b), the aggregate diameter and dispersity


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values were lowest for the all periphery branched C1-(PEG-[G2]-LE4)1 (64 nm, 0.32), then highest for C2-(PEG-[G1]-LE2) (73 nm, 0.34) with branching at both the core and the periphery, and intermediate for C4-(PEG-LE)4 (70 nm, 0.33) with branching exclusively at the core. Thus, as branching location changes from being entirely at the core (C4-(PEG-LE)4) to entirely at the periphery (C1-(PEG-[G2]-LE4)1), the aggregate size increases slightly for the C2(PEG-[G1]-LE2) before a more significant reduction is observed. A possible interpretation for the reduced aggregate size for the [G2] peripherally branched amphiphiles is the increased spatial demand of the large, semi-rigid dendritic wedge.68 The bulky head-group may impart sufficient steric force at the polymers polar/non-polar interface to impose an inherent unimer radius of curvature69-71; hence, the wedge-like amphiphile conformation (favoring bending towards the PEG core) would encourage the assembly of smaller aggregates.65 Indeed, a similar trend can be seen comparing the octa-laurylated amphiphiles (Fig. 8c); the diameter of the [G2] dendronized C2-(PEG-[G2]-LE4)2 (28 nm) is moderately smaller than the more core-branched analog of the same lauryl functionality, C4-(PEG-[G1]-LE2)4 (33 nm). However, these subtle difference in aggregate size are small relative to the error measured and much less significant than the general trend with respect to increased branching/laurate ester content.

Figure 8. DLS and AFM size (top, nm) and dispersity (bottom) values with standard deviation for branched amphiphile aggregates, plotted by equivalent overall branching number and φLE; (a) 2 laurate ester functionalities; (b) 4 laurate ester functionalities; (c) 8 laurate ester functionalities.


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Overall, the number of branches (and corresponding number of lauryl groups), rather than the location of the branches, appears to be the dominant factor in determining self-assembly behavior. This trend can be seen clearly when grouping the amphiphiles according to the number of lauryl groups and comparing aggregate diameter by dynamic light scattering. The bis-laurylated amphiphiles exhibit sizes in the ~120 nm range, while the tetra-laurylated amphiphiles exhibit a DLS diameter of ~70 nm. Furthermore, the octa-laurylated amphiphiles exhibit diameters of ~30 nm and the most branched species (with 16 lauryl groups) exhibits a diameter of ~18 nm. The AFM data shows very similar trends, with an approximate halving of the aggregate size with each doubling of the lauryl end groups. While the results for this particular library appear very conclusive, this study only probes three different branched cores and three different generations of peripheral dendrons, with no variation in PEG molecular weight or the fatty acid chain length. Thus, a broader library will need to be investigated, both computationally and experimentally, to further elucidate these trends and the role of branching in self-assembly.

CONCLUSIONS A library of architecturally diverse amphiphiles was generated featuring exact control of branching multiplicity at both the polymer core and periphery. Material characterization by MALDI-TOF MS, GPC and NMR confirmed the structural and chemical purity of the amphiphiles, allowing for the aggregation behavior to be assessed with respect to total branching multiplicity and branching location. By AFM and DLS analysis, it was found that reverse micelle size and dispersity is predominantly controlled by total branching number and


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concomitant mass fraction of the non-polar groups, with greater overall amphiphile branching/lipophilicity yielding aggregates of smaller diameter and narrower dispersity. These findings were correlated to computational modeling data for unimer SASA, which showed consistent %PEG solvent exposure for amphiphiles of equivalent total branches/number of lauryl groups. Contributions related to the location of branching were observed to only moderately influence self-assembly aggregate size and dispersity, relative to the significant effect of total branching content. However, future studies will need to be conducted to ascertain the discrete contribution of total branch number versus the non-polar group mass fraction in directing reverse micelle self-assembly trends of the branched polymer library.

ASSOCIATED CONTENT Supporting Information. Experimental data supplement containing material characterization spectra (MALDI-TOF MS, NMR, GPC), AFM and DLS controls and summary data. Computational modeling supplement detailing approach and parameters used in simulation models. ACKNOWLEDGEMENTS We would like to thank the National Science Foundation for their funding in support of this work (CHE-1412439, IAA-1430280), acquisition of MALDI-TOF MS instrument capabilities (CHE-0619770 (MRI)) and graduate fellowship support (KAK, Bioinnovation IGERT, DGE1144646). We also acknowledge and thank Baraka Lwoya and Md. Fakar Uddin (Tulane Chemical Engineering) for their assistance in AFM data collection, Wayne Reed and Daniel


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(55) Downing, D. T. Lipid and Protein Structures in the Permeability Barrier of Mammalian Epidermis. J. Lipid Res. 1992, 33, 301-313. (56) Montaudo, G.; Samperi, F.; Montaudo, M. S. Characterization of Synthetic Polymers by MALDI-MS. Prog. Polym. Sci. 2006, 31, 277-357. (57) Li, Y.; Hoskins, J. N.; Sreerama, S. G.; Grayson, M. A.; Grayson, S. M. The Identification of Synthetic Homopolymer End Groups and Verification of their Transformations Using MALDI-TOF Mass Spectrometry. J. Mass Spectrom. 2010, 45, 587-611. (58) Zimm, B. H.; Stockmayer, W. H. The Dimensions of Chain Molecules Containing Branches and Rings. J. Chem. Phys. 1949, 17, 1301-1314. (59) Comanita, B.; Noren, B.; Roovers, J. Star Poly(ethylene oxide)s from Carbosilane Dendrimers. Macromolecules 1999, 32, 1069-1072. (60) Jones, M. C.; Gao, H.; Leroux, J. C. Reverse Polymeric Micelles for Pharmaceutical Applications. J. Controlled Release 2008, 132, 208-215. (61) Minatti, E.; Viville, P.; Borsali, R.; Schappacher, M.; Deffieux, A.; Lazzaroni, R. Micellar Morphological Changes Promoted by Cyclization of PS-b-PI Copolymer: DLS and AFM Experiments. Macromolecules 2003, 36, 4125-4133. (62) Jain, S.; Bates, F. S. Consequences of Nonergodicity in Aqueous Binary PEO−PB Micellar Dispersions. Macromolecules 2004, 37, 1511-1523. (63) Wilson, D. L.; Kump, K. S.; Eppell, S. J.; Marchant, R. E. Morphological Restoration of Atomic Force Microscopy Images. Langmuir 1995, 11, 265-272. (64) Riess, G. Micellization of Block Copolymers. Prog. Polym. Sci. 2003, 28, 1107-1170. (65) Israelachvili, J. N.; Mitchell, D. J.; Ninham, B. W. Theory of Self-Assembly of Hydrocarbon Amphiphiles into Micelles and Bilayers. J. Chem. Soc., Faraday Trans. 2 1976, 72, 1525-1568. (66) Alexandridis, P.; Lindman, B. Amphiphilic Block Copolymers: Self-Assembly and Applications; Elsevier: Amsterdam, 2000. (67) Bogusz, S.; Venable, R. M.; Pastor, R. W. Molecular Dynamics Simulations of Octyl Glucoside Micelles: Structural Properties. J. Phys. Chem. B 2000, 104, 5462-5470. (68) Trappmann, B.; Ludwig, K.; Radowski, M. R.; Shukla, A.; Mohr, A.; Rehage, H.; Böttcher, C.; Haag, R. A New Family of Nonionic Dendritic Amphiphiles Displaying Unexpected Packing Parameters in Micellar Assemblies. J. Am. Chem. Soc. 2010, 132, 11119-11124. (69) Hadjichristidis, N.; Iatrou, H.; Behal, S.; Chludzinski, J.; Disko, M.; Garner, R.; Liang, K.; Lohse, D.; Milner, S. Morphology and Miscibility of Miktoarm Styrene-Diene Copolymers and Terpolymers. Macromolecules 1993, 26, 5812-5815.


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(70) Pispas, S.; Hadjichristidis, N. Effect of Architecture on the Micellization Properties of Block Copolymers: A2B Miktoarm Stars vs AB Diblocks. Macromolecules 2000, 33, 17411746. (71) Ge, Z.; Cai, Y.; Yin, J.; Zhu, Z.; Rao, J.; Liu, S. Synthesis and ‘Schizophrenic'Micellization of Double Hydrophilic AB4 Miktoarm Star and AB Diblock Copolymers: Structure and Kinetics of Micellization. Langmuir 2007, 23, 1114-1122.


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FOR TABLE OF CONTENTS USE ONLY “Synthesis and self-assembly of amphiphilic star/linear-dendritic polymers: effect of core-vsperipheral branching on reverse micelle aggregation” Karolina A. Kosakowska, Brittany K. Casey, Julie N. L. Albert, Yang Wang, Henry S. Ashbaugh, Scott M. Grayson


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Scheme 1. General synthesis of branched amphiphile library; modular approach uses divergent dendronization of core molecule functionalities (1-, 2-, and 4-arm PEG) to create linear- and star-dendritic hybrids, followed by ester coupling of lipophilic lauric acid moieties to yield amphiphilic materials. 130x343mm (96 x 96 DPI)


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Scheme 2. Systematic library of branched amphiphile linear- and star-dendritic polymer hybrids, with core and peripheral branching varying along the vertical and horizontal axes, respectively. 175x105mm (96 x 96 DPI)



Figure 1. MALDI-TOF mass spectra of 2-arm PEG derivatives, ionized with Na+ and using α-cyano-4hydroxycinnamic acid as matrix; synthetic functionalization of a single oligomer (n=104) is highlighted through subsequent dendronization/deprotection steps and peripheral laurylation, with corresponding peak shifts in exact agreement with theoretical values. Quantitative end-group transformation is observed throughout each stage of modification. 279x165mm (96 x 96 DPI)


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Figure 2. GPC trace data for 2-arm PEG derivatives; (a) overlay of starting material with [G1] dendronized/deprotected species and (b) overlay of [G1] deprotected analogue (dashed line) with subsequent [G2] dendronized/deprotected species; peak retention time enlarged below to show relative mass shift to end-group character; (c) overlay of starting material trace with [G0], [G1] and [G2] laurylated amphiphiles derived therefrom. 222x308mm (96 x 96 DPI)



Figure 3. 1H NMR spectra monitoring 2-arm PEG core end-group transformations for subsequent [G1] dendronized analogues; (a) 2-arm PEG starting material, C2-(PEG-OH)2; (b) first generation dendronized product, C2-(PEG-[G1]-Ph)2; (c) deprotected dendronized product, C2-(PEG-[G1]-OH2)2; and (d) laurate ester functionalized product, C2-(PEG-[G1]-LE2)2. All spectra were collected in (CD3)2SO; * indicates PEG backbone sideband. 279x169mm (96 x 96 DPI)


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Figure 4. Representative AFM height sensor images (1 µm2) of branched amphiphile solid-state aggregates with corresponding particle diameter distributions below, compiled from multiple images; (a) C1-(PEGLE)1; (b) C1-(PEG-[G1]-LE2)1; (c) C1-(PEG-[G2]-LE4)1; (d) C2-(PEG-LE)2; (e) C2-(PEG-[G1]-LE2)2; (f) C2-(PEG-[G2]-LE4)2; (g) C4-(PEG-LE)4; (h) C4-(PEG-[G1]-LE2)4; (i) C4-(PEG-[G2]-LE4)4. 128x192mm (96 x 96 DPI)



Figure 5. DLS diameter and dispersity values with standard deviation for branched amphiphile aggregates, plotted by (a) and (b) core branching; (c) and (d) peripheral branching. 131x140mm (96 x 96 DPI)


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Figure 6. Branched amphiphile SASA toluene exposure fraction of unimer solvatophobic PEG domain (solid line) and solvatophilic alkyl domain (dashed line) plotted by (a) core branching; (b) peripheral branching. 130x76mm (96 x 96 DPI)



Figure 7. Branched amphiphile SASA toluene exposure fraction (left axis) of unimer solvatophobic PEG (black symbol) and solvatophilic alkyl (gray symbol) domains and corresponding experimentally-obtained reverse micelle diameters (nm, right axis, open red symbol), plotted as a function of total amphiphile alkyl number (1 through 16). 128x93mm (96 x 96 DPI)


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Figure 8. DLS and AFM size (top, nm) and dispersity (bottom) values with standard deviation for branched amphiphile aggregates, plotted by equivalent overall branching number and φLE; (a) 2 laurate ester functionalities; (b) 4 laurate ester functionalities; (c) 8 laurate ester functionalities. 278x68mm (96 x 96 DPI)


linear-dendritic

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